:: BOR_CANT semantic presentation

begin

definition
let D be ( ( ) ( ) set ) ;
let x, y be ( ( ext-real ) ( ext-real ) number ) ;
let a, b be ( ( ) ( ) Element of D : ( ( ) ( ) set ) ) ;
:: original: IFGT
redefine func IFGT (x,y,a,b) -> ( ( ) ( ) Element of D : ( ( V28() ) ( V28() ) set ) ) ;
end;

theorem :: BOR_CANT:1
for k being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) )
for x being ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) st k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) is odd & x : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) > 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & x : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) <= 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds
(((- x : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) rExpSeq) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . (k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) + (((- x : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) rExpSeq) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . (k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) >= 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;

theorem :: BOR_CANT:2
for x being ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) holds 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + x : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) <= exp_R : ( ( Function-like V18( REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V18( REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . x : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

definition
let s be ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Real_Sequence) ;
func JSum s -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Real_Sequence) means :: BOR_CANT:def 1
for d being ( ( natural ) ( epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative ) Nat) holds it : ( ( ) ( V28() ) Element of COMPLEX : ( ( ) ( non empty V34() V70() V76() ) set ) ) . d : ( ( natural ) ( epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative ) Nat) : ( ( ) ( ) set ) = Sum ((- (s : ( ( V28() ) ( V28() ) set ) . d : ( ( natural ) ( epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative ) Nat) ) : ( ( ) ( ) set ) ) : ( ( V28() ) ( V28() ) set ) rExpSeq) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;
end;

theorem :: BOR_CANT:3
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds (Partial_Product (JSum (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Real_Sequence) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = exp_R : ( ( Function-like V18( REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V18( REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . (- ((Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

theorem :: BOR_CANT:4
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds (Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) <= (Partial_Product (JSum (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Real_Sequence) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

definition
let n1, n2 be ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
func Special_Function (n1,n2) -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) means :: BOR_CANT:def 2
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds it : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) = IFGT (n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,n1 : ( ( V28() ) ( V28() ) set ) ,(n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + n2 : ( ( ) ( V28() ) Element of COMPLEX : ( ( ) ( non empty V34() V70() V76() ) set ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

definition
let k be ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
func Special_Function2 k -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) means :: BOR_CANT:def 3
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds it : ( ( ) ( V28() ) Element of COMPLEX : ( ( ) ( non empty V34() V70() V76() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) = n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + k : ( ( V28() ) ( V28() ) set ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

definition
let k be ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
func Special_Function3 k -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) means :: BOR_CANT:def 4
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds it : ( ( ) ( V28() ) Element of COMPLEX : ( ( ) ( non empty V34() V70() V76() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) = IFGT (n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,k : ( ( V28() ) ( V28() ) set ) ,0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

definition
let n1, n2 be ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
func Special_Function4 (n1,n2) -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) means :: BOR_CANT:def 5
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds it : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) = IFGT (n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,(n1 : ( ( V28() ) ( V28() ) set ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,(n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + n2 : ( ( ) ( V28() ) Element of COMPLEX : ( ( ) ( non empty V34() V70() V76() ) set ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

registration
let n1, n2 be ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
cluster Special_Function (n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) -> Function-like one-to-one V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
cluster Special_Function4 (n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) -> Function-like one-to-one V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

registration
let n be ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
cluster Special_Function2 n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) -> Function-like one-to-one V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

registration
let Omega be ( ( non empty ) ( non empty ) set ) ;
let Sigma be ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ;
let s be ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
let A be ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
cluster A : ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ^\ s : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) set ) -> Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

theorem :: BOR_CANT:5
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n, n1, n2 being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds
( ( for A, B being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) st n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) > n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & B : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) = A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (Special_Function (n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) )) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like one-to-one V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) holds
(Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * B : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = ((Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) * ((Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ^\ ((n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,b7 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) )) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . ((n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) - n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) - 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) : ( ( ) ( V28() real ext-real ) set ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) & ( for A, B, C being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for e being ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) > n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & C : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) = A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * e : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) & B : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) = C : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (Special_Function (n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ,n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) )) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like one-to-one V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) holds
(Partial_Intersection B : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) = ((Partial_Intersection C : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) /\ ((Partial_Intersection (C : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ^\ ((n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,b9 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) )) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . ((n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) - n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) - 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) : ( ( ) ( ) set ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ;

definition
let Omega be ( ( non empty ) ( non empty ) set ) ;
let Sigma be ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ;
let Prob be ( ( ) ( non empty Relation-like Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) V18(Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
let A be ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
pred A is_all_independent_wrt Prob means :: BOR_CANT:def 6
for B being ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( ) ( ) set ) ) st ex e being ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V59() V60() V61() V62() ) sequence of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st
( e : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) is one-to-one & ( for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds A : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . (e : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of Sigma : ( ( ) ( ) set ) ) = B : ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of Sigma : ( ( ) ( ) set ) ) ) ) holds
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds (Partial_Product (Prob : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) * B : ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = Prob : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . ((Partial_Intersection B : ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of Sigma : ( ( ) ( ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;
end;

theorem :: BOR_CANT:6
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n, n1, n2 being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) > n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) is_all_independent_wrt Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) holds
Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (((Partial_Intersection (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) /\ ((Partial_Intersection (A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ^\ ((n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,b4 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) )) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . ((n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) - n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) - 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = ((Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) * ((Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ^\ ((n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + n2 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,b4 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) )) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . ((n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) - n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) - 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) : ( ( ) ( V28() real ext-real ) set ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

theorem :: BOR_CANT:7
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds (Partial_Intersection (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) = ((Partial_Union A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ` : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ;

theorem :: BOR_CANT:8
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . ((Partial_Intersection (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) - (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . ((Partial_Union A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

definition
let X be ( ( ) ( ) set ) ;
let A be ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
func Union_Shift_Seq A -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) means :: BOR_CANT:def 7
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds it : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) = Union (A : ( ( ) ( ) set ) ^\ n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ,A : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool X : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ;
end;

registration
let Omega be ( ( non empty ) ( non empty ) set ) ;
let Sigma be ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ;
let A be ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
cluster Union_Shift_Seq A : ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) -> Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

definition
let Omega be ( ( non empty ) ( non empty ) set ) ;
let Sigma be ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ;
let A be ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
func @lim_sup A -> ( ( ) ( ) Event of Sigma : ( ( ) ( ) set ) ) equals :: BOR_CANT:def 8
@Intersection (Union_Shift_Seq A : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of Sigma : ( ( ) ( ) set ) ) ;
end;

definition
let X be ( ( ) ( ) set ) ;
let A be ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
func Intersect_Shift_Seq A -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) means :: BOR_CANT:def 9
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds it : ( ( A : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined A : ( ( ) ( ) set ) -valued K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) = Intersection (A : ( ( ) ( ) set ) ^\ n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ,A : ( ( ) ( ) set ) )) : ( ( ) ( ) Element of bool X : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ;
end;

registration
let Omega be ( ( non empty ) ( non empty ) set ) ;
let Sigma be ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ;
let A be ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
cluster Intersect_Shift_Seq A : ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) -> Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ;
end;

definition
let Omega be ( ( non empty ) ( non empty ) set ) ;
let Sigma be ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ;
let A be ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
func @lim_inf A -> ( ( ) ( ) Event of Sigma : ( ( ) ( ) set ) ) equals :: BOR_CANT:def 10
Union (Intersect_Shift_Seq A : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool Omega : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ;
end;

theorem :: BOR_CANT:9
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds (Intersect_Shift_Seq (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) = ((Union_Shift_Seq A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ` : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ;

theorem :: BOR_CANT:10
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) is_all_independent_wrt Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) holds
Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . ((Partial_Intersection (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = (Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

theorem :: BOR_CANT:11
for X being ( ( ) ( ) set )
for A being ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool X : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds
( superior_setsequence A : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) non-ascending ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) = Union_Shift_Seq A : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & inferior_setsequence A : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) non-descending ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) = Intersect_Shift_Seq A : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool b1 : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ;

theorem :: BOR_CANT:12
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) holds
( superior_setsequence A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) non-ascending ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) = Union_Shift_Seq A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & inferior_setsequence A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) non-descending ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) = Intersect_Shift_Seq A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ;

definition
let Omega be ( ( non empty ) ( non empty ) set ) ;
let Sigma be ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ;
let Prob be ( ( ) ( non empty Relation-like Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) V18(Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
let A be ( ( Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) -valued K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool Omega : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) ) ;
func Sum_Shift_Seq (Prob,A) -> ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Real_Sequence) means :: BOR_CANT:def 11
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds it : ( ( Function-like ) ( Relation-like Omega : ( ( ) ( ) set ) -defined Prob : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V59() V60() V61() ) Element of bool [:Omega : ( ( ) ( ) set ) ,Prob : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( Relation-like ) set ) : ( ( ) ( non empty ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = Sum (Prob : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) * (A : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ^\ n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ,A : ( ( Sigma : ( ( ) ( ) set ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) Element of bool (bool Omega : ( ( ) ( ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) )) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined Sigma : ( ( ) ( ) set ) -valued REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;
end;

theorem :: BOR_CANT:13
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) st Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) is convergent holds
( Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (@lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & lim (Sum_Shift_Seq (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ,A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) )) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Real_Sequence) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & Sum_Shift_Seq (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ,A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Real_Sequence) is convergent ) ;

theorem :: BOR_CANT:14
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) ) holds
( ( for X being ( ( ) ( ) set )
for A being ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool X : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) )
for x being ( ( ) ( ) set ) holds
( ex k being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st x : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) in (A : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) ^\ n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,b4 : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) )) . k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued ) Element of K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) iff ex k being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st
( k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) >= n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & x : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) in A : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) . k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued ) Element of K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ) ) & ( for X being ( ( ) ( ) set )
for A being ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool X : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) )
for x being ( ( ) ( ) set ) holds
( x : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) in Intersection (Union_Shift_Seq A : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued ) Element of bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( non empty V94() ) set ) ) iff for m being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ex n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st
( n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) >= m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & x : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) in A : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued ) Element of K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ) ) & ( for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for x being ( ( ) ( ) set ) holds
( x : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) in @Intersection (Union_Shift_Seq A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) iff for m being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ex n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st
( n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) >= m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & x : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) in A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) ) ) & ( for X being ( ( ) ( ) set )
for A being ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool X : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) )
for x being ( ( ) ( ) set ) holds
( x : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) in Union (Intersect_Shift_Seq A : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued ) Element of bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( non empty V94() ) set ) ) iff ex n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st
for k being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) >= n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds
x : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) in A : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) . k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued ) Element of K496(b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b3 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ) & ( for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for x being ( ( ) ( ) set ) holds
( x : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) in Union (Intersect_Shift_Seq A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) iff ex n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st
for k being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) >= n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds
x : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) in A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) ) & ( for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for x being ( ( ) ( ) Element of Omega : ( ( non empty ) ( non empty ) set ) ) holds
( x : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) in Union (Intersect_Shift_Seq (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) iff ex n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st
for k being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) st k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) >= n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds
not x : ( ( ) ( ) Element of b1 : ( ( non empty ) ( non empty ) set ) ) in A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) ) ) ;

theorem :: BOR_CANT:15
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) holds
( lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) = @lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) & lim_inf A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) = @lim_inf A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) & @lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) = (@lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ` : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) & (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (@lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) + (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (@lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) set ) + (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) set ) : ( ( ) ( V28() real ext-real ) set ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ;

theorem :: BOR_CANT:16
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) holds
( ( Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) is convergent implies ( Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ) & ( A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) is_all_independent_wrt Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) & Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) is divergent_to+infty implies ( Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ) ) ;

theorem :: BOR_CANT:17
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) st not Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) is convergent & A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) is_all_independent_wrt Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) holds
( Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) & Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ;

theorem :: BOR_CANT:18
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) st A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) is_all_independent_wrt Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) holds
( ( Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) or Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_inf (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) & ( Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 0 : ( ( ) ( empty Relation-like non-empty empty-yielding RAT : ( ( ) ( non empty V34() V70() V71() V72() V73() V76() ) set ) -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V30() V31() V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) or Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . (lim_sup A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool b1 : ( ( non empty ) ( non empty ) set ) : ( ( ) ( non empty V94() ) set ) ) : ( ( ) ( V28() real ext-real ) set ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ) ;

theorem :: BOR_CANT:19
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n1, n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds (Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ^\ (n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) M16(K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,b4 : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) )) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) <= ((Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . ((n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) + n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) - ((Partial_Sums (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

theorem :: BOR_CANT:20
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . ((Intersect_Shift_Seq (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) - (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . ((Union_Shift_Seq A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ;

theorem :: BOR_CANT:21
for Omega being ( ( non empty ) ( non empty ) set )
for Sigma being ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of Omega : ( ( non empty ) ( non empty ) set ) )
for Prob being ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for A being ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of Sigma : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) )
for n being ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) holds
( ( Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) is_all_independent_wrt Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) implies Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . ((Partial_Intersection A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = (Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) & ( A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) is_all_independent_wrt Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) implies 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) - (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) . ((Partial_Union A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) : ( ( ) ( ) Event of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) = (Partial_Product (Prob : ( ( ) ( non empty Relation-like b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) V18(b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Probability of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) * (Complement A : ( ( b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) SetSequence of b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined b2 : ( ( non empty compl-closed sigma-multiplicative ) ( non empty compl-closed sigma-multiplicative ) SigmaField of b1 : ( ( non empty ) ( non empty ) set ) ) -valued K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,K496(b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) Element of bool (bool b1 : ( ( non empty ) ( non empty ) set ) ) : ( ( ) ( non empty V94() ) set ) : ( ( ) ( non empty V94() ) set ) ) :] : ( ( ) ( non empty Relation-like ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( Function-like V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) -defined REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) -valued Function-like V17( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) V18( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) , REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) V59() V60() V61() ) Element of bool [:NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ,REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) :] : ( ( ) ( non empty Relation-like V59() V60() V61() ) set ) : ( ( ) ( non empty V94() ) set ) ) . n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() ) Element of bool REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) : ( ( ) ( non empty V94() ) set ) ) ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V70() V71() V72() V76() ) set ) ) ) ) ;