:: BOR_CANT semantic presentation

REAL is non empty V34() V70() V71() V72() V76() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() Element of bool REAL
bool REAL is non empty V94() set
COMPLEX is non empty V34() V70() V76() set
RAT is non empty V34() V70() V71() V72() V73() V76() set
INT is non empty V34() V70() V71() V72() V73() V74() V76() set
[:COMPLEX,COMPLEX:] is non empty Relation-like V59() set
bool [:COMPLEX,COMPLEX:] is non empty V94() set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty Relation-like V59() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty V94() set
[:REAL,REAL:] is non empty Relation-like V59() V60() V61() set
bool [:REAL,REAL:] is non empty V94() set
[:[:REAL,REAL:],REAL:] is non empty Relation-like V59() V60() V61() set
bool [:[:REAL,REAL:],REAL:] is non empty V94() set
[:RAT,RAT:] is non empty Relation-like RAT -valued V59() V60() V61() set
bool [:RAT,RAT:] is non empty V94() set
[:[:RAT,RAT:],RAT:] is non empty Relation-like RAT -valued V59() V60() V61() set
bool [:[:RAT,RAT:],RAT:] is non empty V94() set
[:INT,INT:] is non empty Relation-like RAT -valued INT -valued V59() V60() V61() set
bool [:INT,INT:] is non empty V94() set
[:[:INT,INT:],INT:] is non empty Relation-like RAT -valued INT -valued V59() V60() V61() set
bool [:[:INT,INT:],INT:] is non empty V94() set
[:NAT,NAT:] is non empty Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
[:[:NAT,NAT:],NAT:] is non empty Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:[:NAT,NAT:],NAT:] is non empty V94() set
omega is non empty epsilon-transitive epsilon-connected ordinal V70() V71() V72() V73() V74() V75() V76() set
bool omega is non empty V94() set
bool NAT is non empty V94() set
K246() is set
1 is 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
[:NAT,REAL:] is non empty Relation-like V59() V60() V61() set
bool [:NAT,REAL:] is non empty V94() set
[:NAT,COMPLEX:] is non empty Relation-like V59() set
bool [:NAT,COMPLEX:] is non empty V94() set
bool (bool REAL) is non empty V94() set
[:COMPLEX,REAL:] is non empty Relation-like V59() V60() V61() set
bool [:COMPLEX,REAL:] is non empty V94() set
{} is empty Relation-like non-empty empty-yielding RAT -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() set
K2({},1) is non empty V70() V71() V72() V73() V74() V75() set
0 is empty Relation-like non-empty empty-yielding RAT -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
2 is 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
3 is 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
exp_R is non empty Relation-like REAL -defined REAL -valued Function-like V17( REAL ) V18( REAL , REAL ) V59() V60() V61() Element of bool [:REAL,REAL:]
exp_R 0 is V28() real ext-real Element of REAL
exp_R . 0 is V28() real ext-real Element of REAL
0 ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prod_real_n . 0 is V28() real ext-real Element of REAL
K234(0) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real Function-yielding V33() V34() V41( 0 ) V42() V43() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() set
K436(K234(0)) is V28() set
1 ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n . 1 is V28() real ext-real Element of REAL
K234(1) is Relation-like NAT -defined RAT -valued Function-like V34() V41(1) V42() V43() V59() V60() V61() V62() set
K436(K234(1)) is V28() set
Omega is set
Sigma is ext-real set
Prob is ext-real set
A is Element of Omega
n is Element of Omega
IFGT (Sigma,Prob,A,n) is set
Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega + 1 is 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
Omega + 2 is 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
Sigma is V28() real ext-real Element of REAL
- Sigma is V28() real ext-real Element of REAL
(- Sigma) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
((- Sigma) rExpSeq) . (Omega + 1) is V28() real ext-real Element of REAL
((- Sigma) rExpSeq) . (Omega + 2) is V28() real ext-real Element of REAL
(((- Sigma) rExpSeq) . (Omega + 1)) + (((- Sigma) rExpSeq) . (Omega + 2)) is V28() real ext-real Element of REAL
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * Prob) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
Prob + 1 is 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
2 * (Prob + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * (Prob + 1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(- Sigma) |^ n is V28() real ext-real Element of REAL
K235(n,(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(n) V42() V43() V59() set
K436(K235(n,(- Sigma))) is V28() set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
2 * 0 is empty Relation-like non-empty empty-yielding RAT -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() even Element of NAT
(- Sigma) |^ (2 * 0) is V28() real ext-real Element of REAL
K235((2 * 0),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(2 * 0) V42() V43() V59() set
K436(K235((2 * 0),(- Sigma))) is V28() set
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(- Sigma) |^ (2 * B2) is V28() real ext-real Element of REAL
K235((2 * B2),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(2 * B2) V42() V43() V59() set
K436(K235((2 * B2),(- Sigma))) is V28() set
B2 + 1 is 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
2 * (B2 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(- Sigma) |^ (2 * (B2 + 1)) is V28() real ext-real Element of REAL
K235((2 * (B2 + 1)),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(2 * (B2 + 1)) V42() V43() V59() set
K436(K235((2 * (B2 + 1)),(- Sigma))) is V28() set
(2 * B2) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(- Sigma) |^ ((2 * B2) + 2) is V28() real ext-real Element of REAL
K235(((2 * B2) + 2),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41((2 * B2) + 2) V42() V43() V59() set
K436(K235(((2 * B2) + 2),(- Sigma))) is V28() set
(- Sigma) |^ 2 is V28() real ext-real Element of REAL
K235(2,(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(2) V42() V43() V59() set
K436(K235(2,(- Sigma))) is V28() set
((- Sigma) |^ (2 * B2)) * ((- Sigma) |^ 2) is V28() real ext-real Element of REAL
(- Sigma) * (- Sigma) is V28() real ext-real Element of REAL
Sigma |^ (Omega + 2) is V28() real ext-real Element of REAL
K235((Omega + 2),Sigma) is Relation-like NAT -defined Function-like V34() V41(Omega + 2) V42() V43() V59() set
K436(K235((Omega + 2),Sigma)) is V28() set
(- Sigma) |^ (Omega + 1) is V28() real ext-real Element of REAL
K235((Omega + 1),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(Omega + 1) V42() V43() V59() set
K436(K235((Omega + 1),(- Sigma))) is V28() set
(Sigma |^ (Omega + 2)) / ((- Sigma) |^ (Omega + 1)) is V28() real ext-real Element of COMPLEX
(Omega + 1) + 1 is 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
Sigma |^ ((Omega + 1) + 1) is V28() real ext-real Element of REAL
K235(((Omega + 1) + 1),Sigma) is Relation-like NAT -defined Function-like V34() V41((Omega + 1) + 1) V42() V43() V59() set
K436(K235(((Omega + 1) + 1),Sigma)) is V28() set
Sigma |^ (Omega + 1) is V28() real ext-real Element of REAL
K235((Omega + 1),Sigma) is Relation-like NAT -defined Function-like V34() V41(Omega + 1) V42() V43() V59() set
K436(K235((Omega + 1),Sigma)) is V28() set
(Sigma |^ (Omega + 1)) * Sigma is V28() real ext-real Element of REAL
Sigma * ((- Sigma) |^ (Omega + 1)) is V28() real ext-real Element of REAL
((- Sigma) |^ (Omega + 1)) " is V28() real ext-real Element of REAL
(Sigma * ((- Sigma) |^ (Omega + 1))) * (((- Sigma) |^ (Omega + 1)) ") is V28() real ext-real Element of REAL
((- Sigma) |^ (Omega + 1)) * (((- Sigma) |^ (Omega + 1)) ") is V28() real ext-real Element of REAL
Sigma * (((- Sigma) |^ (Omega + 1)) * (((- Sigma) |^ (Omega + 1)) ")) is V28() real ext-real Element of REAL
((- Sigma) |^ (Omega + 1)) / ((- Sigma) |^ (Omega + 1)) is V28() real ext-real Element of COMPLEX
(Omega + 2) ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n . (Omega + 2) is V28() real ext-real Element of REAL
K234((Omega + 2)) is Relation-like NAT -defined RAT -valued Function-like V34() V41(Omega + 2) V42() V43() V59() V60() V61() V62() set
K436(K234((Omega + 2))) is V28() set
(Omega + 1) ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n . (Omega + 1) is V28() real ext-real Element of REAL
K234((Omega + 1)) is Relation-like NAT -defined RAT -valued Function-like V34() V41(Omega + 1) V42() V43() V59() V60() V61() V62() set
K436(K234((Omega + 1))) is V28() set
((Omega + 2) !) / ((Omega + 1) !) is non empty V28() real ext-real positive non negative Element of COMPLEX
(Omega + 1) + 1 is 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
((Omega + 1) + 1) * ((Omega + 1) !) is 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
((Omega + 1) !) " is non empty V28() real ext-real positive non negative Element of REAL
((Omega + 2) !) * (((Omega + 1) !) ") is non empty V28() real ext-real positive non negative Element of REAL
((Omega + 1) !) * (((Omega + 1) !) ") is non empty V28() real ext-real positive non negative Element of REAL
((Omega + 1) + 1) * (((Omega + 1) !) * (((Omega + 1) !) ")) is non empty V28() real ext-real positive non negative Element of REAL
((Omega + 1) !) / ((Omega + 1) !) is non empty V28() real ext-real positive non negative Element of COMPLEX
((Omega + 1) + 1) * 1 is 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
((- Sigma) |^ (Omega + 1)) " is V28() real ext-real Element of REAL
(Sigma |^ (Omega + 2)) * (((- Sigma) |^ (Omega + 1)) ") is V28() real ext-real Element of REAL
((Omega + 1) !) " is non empty V28() real ext-real positive non negative Element of REAL
(((Omega + 1) !) ") * ((Omega + 2) !) is non empty V28() real ext-real positive non negative Element of REAL
(Sigma |^ (Omega + 2)) / ((Omega + 2) !) is V28() real ext-real Element of COMPLEX
(((Omega + 1) !) ") / (((- Sigma) |^ (Omega + 1)) ") is V28() real ext-real Element of COMPLEX
(((Omega + 1) !) ") * 1 is non empty V28() real ext-real positive non negative Element of REAL
1 / ((Omega + 1) !) is non empty V28() real ext-real positive non negative Element of COMPLEX
(((- Sigma) |^ (Omega + 1)) ") " is V28() real ext-real Element of REAL
(1 / ((Omega + 1) !)) * ((((- Sigma) |^ (Omega + 1)) ") ") is V28() real ext-real Element of REAL
1 * (((Omega + 1) !) ") is non empty V28() real ext-real positive non negative Element of REAL
((- Sigma) |^ (Omega + 1)) / ((Omega + 1) !) is V28() real ext-real Element of COMPLEX
Sigma rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Sigma rExpSeq) . (Omega + 2) is V28() real ext-real Element of REAL
((Sigma rExpSeq) . (Omega + 2)) - (((- Sigma) rExpSeq) . (Omega + 1)) is V28() real ext-real Element of REAL
(((- Sigma) rExpSeq) . (Omega + 1)) - (((- Sigma) rExpSeq) . (Omega + 1)) is V28() real ext-real Element of REAL
- (((Sigma rExpSeq) . (Omega + 2)) - (((- Sigma) rExpSeq) . (Omega + 1))) is V28() real ext-real Element of REAL
- ((Sigma rExpSeq) . (Omega + 2)) is V28() real ext-real Element of REAL
2 * 0 is empty Relation-like non-empty empty-yielding RAT -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() even Element of NAT
(2 * 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
(- Sigma) |^ ((2 * 0) + 1) is V28() real ext-real Element of REAL
K235(((2 * 0) + 1),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41((2 * 0) + 1) V42() V43() V59() set
K436(K235(((2 * 0) + 1),(- Sigma))) is V28() set
Sigma |^ ((2 * 0) + 1) is V28() real ext-real Element of REAL
K235(((2 * 0) + 1),Sigma) is Relation-like NAT -defined Function-like V34() V41((2 * 0) + 1) V42() V43() V59() set
K436(K235(((2 * 0) + 1),Sigma)) is V28() set
- (Sigma |^ ((2 * 0) + 1)) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
Sigma |^ ((2 * n) + 1) is V28() real ext-real Element of REAL
K235(((2 * n) + 1),Sigma) is Relation-like NAT -defined Function-like V34() V41((2 * n) + 1) V42() V43() V59() set
K436(K235(((2 * n) + 1),Sigma)) is V28() set
- (Sigma |^ ((2 * n) + 1)) is V28() real ext-real Element of REAL
(- Sigma) |^ ((2 * n) + 1) is V28() real ext-real Element of REAL
K235(((2 * n) + 1),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41((2 * n) + 1) V42() V43() V59() set
K436(K235(((2 * n) + 1),(- Sigma))) is V28() set
n + 1 is 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
2 * (n + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * (n + 1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
Sigma |^ ((2 * (n + 1)) + 1) is V28() real ext-real Element of REAL
K235(((2 * (n + 1)) + 1),Sigma) is Relation-like NAT -defined Function-like V34() V41((2 * (n + 1)) + 1) V42() V43() V59() set
K436(K235(((2 * (n + 1)) + 1),Sigma)) is V28() set
- (Sigma |^ ((2 * (n + 1)) + 1)) is V28() real ext-real Element of REAL
(- Sigma) |^ ((2 * (n + 1)) + 1) is V28() real ext-real Element of REAL
K235(((2 * (n + 1)) + 1),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41((2 * (n + 1)) + 1) V42() V43() V59() set
K436(K235(((2 * (n + 1)) + 1),(- Sigma))) is V28() set
((2 * n) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
Sigma |^ (((2 * n) + 1) + 1) is V28() real ext-real Element of REAL
K235((((2 * n) + 1) + 1),Sigma) is Relation-like NAT -defined Function-like V34() V41(((2 * n) + 1) + 1) V42() V43() V59() set
K436(K235((((2 * n) + 1) + 1),Sigma)) is V28() set
(Sigma |^ (((2 * n) + 1) + 1)) * Sigma is V28() real ext-real Element of REAL
- ((Sigma |^ (((2 * n) + 1) + 1)) * Sigma) is V28() real ext-real Element of REAL
(Sigma |^ ((2 * n) + 1)) * Sigma is V28() real ext-real Element of REAL
((Sigma |^ ((2 * n) + 1)) * Sigma) * Sigma is V28() real ext-real Element of REAL
- (((Sigma |^ ((2 * n) + 1)) * Sigma) * Sigma) is V28() real ext-real Element of REAL
((- Sigma) |^ ((2 * n) + 1)) * (- Sigma) is V28() real ext-real Element of REAL
(((- Sigma) |^ ((2 * n) + 1)) * (- Sigma)) * (- Sigma) is V28() real ext-real Element of REAL
(- Sigma) |^ (((2 * n) + 1) + 1) is V28() real ext-real Element of REAL
K235((((2 * n) + 1) + 1),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(((2 * n) + 1) + 1) V42() V43() V59() set
K436(K235((((2 * n) + 1) + 1),(- Sigma))) is V28() set
((- Sigma) |^ (((2 * n) + 1) + 1)) * (- Sigma) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
- (Sigma |^ (Omega + 2)) is V28() real ext-real Element of REAL
(- Sigma) |^ (Omega + 2) is V28() real ext-real Element of REAL
K235((Omega + 2),(- Sigma)) is Relation-like NAT -defined Function-like V34() V41(Omega + 2) V42() V43() V59() set
K436(K235((Omega + 2),(- Sigma))) is V28() set
- ((Sigma |^ (Omega + 2)) / ((Omega + 2) !)) is V28() real ext-real Element of COMPLEX
((Omega + 2) !) " is non empty V28() real ext-real positive non negative Element of REAL
(Sigma |^ (Omega + 2)) * (((Omega + 2) !) ") is V28() real ext-real Element of REAL
- ((Sigma |^ (Omega + 2)) * (((Omega + 2) !) ")) is V28() real ext-real Element of REAL
(- (Sigma |^ (Omega + 2))) * (((Omega + 2) !) ") is V28() real ext-real Element of REAL
(- (Sigma |^ (Omega + 2))) / ((Omega + 2) !) is V28() real ext-real Element of COMPLEX
Omega is V28() real ext-real Element of REAL
1 + Omega is V28() real ext-real Element of REAL
exp_R . Omega is V28() real ext-real Element of REAL
NAT --> (1 + Omega) is non empty Relation-like NAT -defined REAL -valued Function-like constant V17( NAT ) V18( NAT , REAL ) T-Sequence-like V59() V60() V61() convergent Element of bool [:NAT,REAL:]
Omega rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Omega rExpSeq) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (1 + Omega)) . Prob is V28() real ext-real Element of REAL
Prob + 1 is 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
(Partial_Sums (Omega rExpSeq)) . (Prob + 1) is V28() real ext-real Element of REAL
(Partial_Sums (Omega rExpSeq)) . 1 is V28() real ext-real Element of REAL
(Partial_Sums (Omega rExpSeq)) . 0 is V28() real ext-real Element of REAL
0 + 1 is 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
(Omega rExpSeq) . (0 + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Omega rExpSeq)) . 0) + ((Omega rExpSeq) . (0 + 1)) is V28() real ext-real Element of REAL
(Omega rExpSeq) . 0 is V28() real ext-real Element of REAL
(Omega rExpSeq) . 1 is V28() real ext-real Element of REAL
((Omega rExpSeq) . 0) + ((Omega rExpSeq) . 1) is V28() real ext-real Element of REAL
Omega |^ 0 is V28() real ext-real Element of REAL
K235(0,Omega) is Relation-like NAT -defined Function-like V34() V41( 0 ) V42() V43() V59() set
K436(K235(0,Omega)) is V28() set
(Omega |^ 0) / (0 !) is V28() real ext-real Element of COMPLEX
Omega |^ 1 is V28() real ext-real Element of REAL
K235(1,Omega) is Relation-like NAT -defined Function-like V34() V41(1) V42() V43() V59() set
K436(K235(1,Omega)) is V28() set
(Omega |^ 1) / (1 !) is V28() real ext-real Element of COMPLEX
(NAT --> (1 + Omega)) . 0 is V28() real ext-real set
1 + 0 is 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
(Partial_Sums (Omega rExpSeq)) . (1 + 0) is V28() real ext-real Element of REAL
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (1 + Omega)) . A is V28() real ext-real set
1 + A is 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
(Partial_Sums (Omega rExpSeq)) . (1 + A) is V28() real ext-real Element of REAL
A + 1 is 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
(NAT --> (1 + Omega)) . (A + 1) is V28() real ext-real set
1 + (A + 1) is 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
(Partial_Sums (Omega rExpSeq)) . (1 + (A + 1)) is V28() real ext-real Element of REAL
(Partial_Sums (Omega rExpSeq)) . (A + 1) is V28() real ext-real Element of REAL
(A + 1) + 1 is 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
(Omega rExpSeq) . ((A + 1) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Omega rExpSeq)) . (A + 1)) + ((Omega rExpSeq) . ((A + 1) + 1)) is V28() real ext-real Element of REAL
Omega |^ ((A + 1) + 1) is V28() real ext-real Element of REAL
K235(((A + 1) + 1),Omega) is Relation-like NAT -defined Function-like V34() V41((A + 1) + 1) V42() V43() V59() set
K436(K235(((A + 1) + 1),Omega)) is V28() set
((A + 1) + 1) ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n . ((A + 1) + 1) is V28() real ext-real Element of REAL
K234(((A + 1) + 1)) is Relation-like NAT -defined RAT -valued Function-like V34() V41((A + 1) + 1) V42() V43() V59() V60() V61() V62() set
K436(K234(((A + 1) + 1))) is V28() set
(Omega |^ ((A + 1) + 1)) / (((A + 1) + 1) !) is V28() real ext-real Element of COMPLEX
((Omega rExpSeq) . ((A + 1) + 1)) + ((Partial_Sums (Omega rExpSeq)) . (A + 1)) is V28() real ext-real Element of REAL
(Partial_Sums (Omega rExpSeq)) ^\ 1 is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL , Partial_Sums (Omega rExpSeq))
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (1 + Omega)) . Prob is V28() real ext-real Element of REAL
((Partial_Sums (Omega rExpSeq)) ^\ 1) . Prob is V28() real ext-real Element of REAL
Prob + 1 is 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
(Partial_Sums (Omega rExpSeq)) . (Prob + 1) is V28() real ext-real Element of REAL
lim (NAT --> (1 + Omega)) is V28() real ext-real Element of REAL
(NAT --> (1 + Omega)) . 1 is V28() real ext-real Element of REAL
lim ((Partial_Sums (Omega rExpSeq)) ^\ 1) is V28() real ext-real Element of REAL
lim (Partial_Sums (Omega rExpSeq)) is V28() real ext-real Element of REAL
Sum (Omega rExpSeq) is V28() real ext-real Element of REAL
- Omega is V28() real ext-real Element of REAL
1 - (- Omega) is V28() real ext-real Element of REAL
- (- Omega) is V28() real ext-real Element of REAL
exp_R . (- (- Omega)) is V28() real ext-real Element of REAL
Prob is V28() real ext-real Element of REAL
1 - Prob is V28() real ext-real Element of REAL
- Prob is V28() real ext-real Element of REAL
exp_R . (- Prob) is V28() real ext-real Element of REAL
NAT --> (1 - Prob) is non empty Relation-like NAT -defined REAL -valued Function-like constant V17( NAT ) V18( NAT , REAL ) T-Sequence-like V59() V60() V61() convergent Element of bool [:NAT,REAL:]
(- Prob) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums ((- Prob) rExpSeq) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (1 - Prob)) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Partial_Sums ((- Prob) rExpSeq)) . (n + 1) is V28() real ext-real Element of REAL
0 + 1 is 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
(Partial_Sums ((- Prob) rExpSeq)) . (0 + 1) is V28() real ext-real Element of REAL
(Partial_Sums ((- Prob) rExpSeq)) . 0 is V28() real ext-real Element of REAL
((- Prob) rExpSeq) . 1 is V28() real ext-real Element of REAL
((Partial_Sums ((- Prob) rExpSeq)) . 0) + (((- Prob) rExpSeq) . 1) is V28() real ext-real Element of REAL
((- Prob) rExpSeq) . 0 is V28() real ext-real Element of REAL
(((- Prob) rExpSeq) . 0) + (((- Prob) rExpSeq) . 1) is V28() real ext-real Element of REAL
(- Prob) |^ 1 is V28() real ext-real Element of REAL
K235(1,(- Prob)) is Relation-like NAT -defined Function-like V34() V41(1) V42() V43() V59() set
K436(K235(1,(- Prob))) is V28() set
((- Prob) |^ 1) / (1 !) is V28() real ext-real Element of COMPLEX
(- Prob) |^ 0 is V28() real ext-real Element of REAL
K235(0,(- Prob)) is Relation-like NAT -defined Function-like V34() V41( 0 ) V42() V43() V59() set
K436(K235(0,(- Prob))) is V28() set
((- Prob) |^ 0) / (0 !) is V28() real ext-real Element of COMPLEX
(NAT --> (1 - Prob)) . 0 is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (1 - Prob)) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Partial_Sums ((- Prob) rExpSeq)) . (n + 1) is V28() real ext-real Element of REAL
(NAT --> (1 - Prob)) . (n + 1) is V28() real ext-real Element of REAL
(n + 1) + 1 is 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
(Partial_Sums ((- Prob) rExpSeq)) . ((n + 1) + 1) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ is V28() real ext-real Element of REAL
c₉ rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(c₉ rExpSeq) . B2 is V28() real ext-real Element of REAL
c₉ |^ B2 is V28() real ext-real Element of REAL
K235(B2,c₉) is Relation-like NAT -defined Function-like V34() V41(B2) V42() V43() V59() set
K436(K235(B2,c₉)) is V28() set
B2 ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n . B2 is V28() real ext-real Element of REAL
K234(B2) is Relation-like NAT -defined RAT -valued Function-like V34() V41(B2) V42() V43() V59() V60() V61() V62() set
K436(K234(B2)) is V28() set
(c₉ |^ B2) / (B2 !) is V28() real ext-real Element of COMPLEX
c₉ |^ B2 is V28() real ext-real Element of REAL
K235(B2,c₉) is Relation-like NAT -defined Function-like V34() V41(B2) V42() V43() V59() set
K436(K235(B2,c₉)) is V28() set
B2 ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n . B2 is V28() real ext-real Element of REAL
K234(B2) is Relation-like NAT -defined RAT -valued Function-like V34() V41(B2) V42() V43() V59() V60() V61() V62() set
K436(K234(B2)) is V28() set
(c₉ |^ B2) / (B2 !) is V28() real ext-real Element of COMPLEX
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
c₉ |^ B2 is V28() real ext-real Element of REAL
K235(B2,c₉) is Relation-like NAT -defined Function-like V34() V41(B2) V42() V43() V59() set
K436(K235(B2,c₉)) is V28() set
k + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ |^ (k + k) is V28() real ext-real Element of REAL
K235((k + k),c₉) is Relation-like NAT -defined Function-like V34() V41(k + k) V42() V43() V59() set
K436(K235((k + k),c₉)) is V28() set
c₉ |^ k is V28() real ext-real Element of REAL
K235(k,c₉) is Relation-like NAT -defined Function-like V34() V41(k) V42() V43() V59() set
K436(K235(k,c₉)) is V28() set
(c₉ |^ k) * (c₉ |^ k) is V28() real ext-real Element of REAL
c₉ * c₉ is V28() real ext-real Element of REAL
(c₉ * c₉) |^ k is V28() real ext-real Element of REAL
K235(k,(c₉ * c₉)) is Relation-like NAT -defined Function-like V34() V41(k) V42() V43() V59() set
K436(K235(k,(c₉ * c₉))) is V28() set
B2 ! is non empty epsilon-transitive epsilon-connected ordinal natural V28() real ext-real positive non negative Element of REAL
Prod_real_n . B2 is V28() real ext-real Element of REAL
K234(B2) is Relation-like NAT -defined RAT -valued Function-like V34() V41(B2) V42() V43() V59() V60() V61() V62() set
K436(K234(B2)) is V28() set
(c₉ |^ B2) / (B2 !) is V28() real ext-real Element of COMPLEX
n + 2 is 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
((- Prob) rExpSeq) . (n + 2) is V28() real ext-real Element of REAL
((Partial_Sums ((- Prob) rExpSeq)) . (n + 1)) + (((- Prob) rExpSeq) . (n + 2)) is V28() real ext-real Element of REAL
((- Prob) rExpSeq) . ((n + 1) + 1) is V28() real ext-real Element of REAL
((Partial_Sums ((- Prob) rExpSeq)) . (n + 1)) + (((- Prob) rExpSeq) . ((n + 1) + 1)) is V28() real ext-real Element of REAL
(Partial_Sums ((- Prob) rExpSeq)) . (n + 2) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ is V28() real ext-real Element of REAL
1 - c₉ is V28() real ext-real Element of REAL
- c₉ is V28() real ext-real Element of REAL
(- c₉) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums ((- c₉) rExpSeq) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Sums ((- c₉) rExpSeq)) . B2 is V28() real ext-real Element of REAL
2 * 0 is empty Relation-like non-empty empty-yielding RAT -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() even Element of NAT
(2 * 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
(Partial_Sums ((- c₉) rExpSeq)) . ((2 * 0) + 1) is V28() real ext-real Element of REAL
(Partial_Sums ((- c₉) rExpSeq)) . 0 is V28() real ext-real Element of REAL
((- c₉) rExpSeq) . 1 is V28() real ext-real Element of REAL
((Partial_Sums ((- c₉) rExpSeq)) . 0) + (((- c₉) rExpSeq) . 1) is V28() real ext-real Element of REAL
((- c₉) rExpSeq) . 0 is V28() real ext-real Element of REAL
(((- c₉) rExpSeq) . 0) + (((- c₉) rExpSeq) . 1) is V28() real ext-real Element of REAL
(- c₉) |^ 0 is V28() real ext-real Element of REAL
K235(0,(- c₉)) is Relation-like NAT -defined Function-like V34() V41( 0 ) V42() V43() V59() set
K436(K235(0,(- c₉))) is V28() set
((- c₉) |^ 0) / (0 !) is V28() real ext-real Element of COMPLEX
(- c₉) |^ 1 is V28() real ext-real Element of REAL
K235(1,(- c₉)) is Relation-like NAT -defined Function-like V34() V41(1) V42() V43() V59() set
K436(K235(1,(- c₉))) is V28() set
((- c₉) |^ 1) / (1 !) is V28() real ext-real Element of COMPLEX
1 + 0 is 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
((- c₉) rExpSeq) . (1 + 0) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
(Partial_Sums ((- c₉) rExpSeq)) . ((2 * k) + 1) is V28() real ext-real Element of REAL
k + 1 is 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
2 * (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * (k + 1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
(Partial_Sums ((- c₉) rExpSeq)) . ((2 * (k + 1)) + 1) is V28() real ext-real Element of REAL
(2 * k) + 3 is 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
(Partial_Sums ((- c₉) rExpSeq)) . ((2 * k) + 3) is V28() real ext-real Element of REAL
(2 * k) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(Partial_Sums ((- c₉) rExpSeq)) . ((2 * k) + 2) is V28() real ext-real Element of REAL
((2 * k) + 2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
((- c₉) rExpSeq) . (((2 * k) + 2) + 1) is V28() real ext-real Element of REAL
((Partial_Sums ((- c₉) rExpSeq)) . ((2 * k) + 2)) + (((- c₉) rExpSeq) . (((2 * k) + 2) + 1)) is V28() real ext-real Element of REAL
((2 * k) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(Partial_Sums ((- c₉) rExpSeq)) . (((2 * k) + 1) + 1) is V28() real ext-real Element of REAL
((- c₉) rExpSeq) . ((2 * k) + 3) is V28() real ext-real Element of REAL
((Partial_Sums ((- c₉) rExpSeq)) . (((2 * k) + 1) + 1)) + (((- c₉) rExpSeq) . ((2 * k) + 3)) is V28() real ext-real Element of REAL
((- c₉) rExpSeq) . ((2 * k) + 2) is V28() real ext-real Element of REAL
((Partial_Sums ((- c₉) rExpSeq)) . ((2 * k) + 1)) + (((- c₉) rExpSeq) . ((2 * k) + 2)) is V28() real ext-real Element of REAL
(((Partial_Sums ((- c₉) rExpSeq)) . ((2 * k) + 1)) + (((- c₉) rExpSeq) . ((2 * k) + 2))) + (((- c₉) rExpSeq) . ((2 * k) + 3)) is V28() real ext-real Element of REAL
(((- c₉) rExpSeq) . ((2 * k) + 2)) + (((- c₉) rExpSeq) . ((2 * k) + 3)) is V28() real ext-real Element of REAL
((Partial_Sums ((- c₉) rExpSeq)) . ((2 * k) + 1)) + ((((- c₉) rExpSeq) . ((2 * k) + 2)) + (((- c₉) rExpSeq) . ((2 * k) + 3))) is V28() real ext-real Element of REAL
((- c₉) rExpSeq) . (((2 * k) + 1) + 1) is V28() real ext-real Element of REAL
((2 * k) + 1) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
((- c₉) rExpSeq) . (((2 * k) + 1) + 2) is V28() real ext-real Element of REAL
(((- c₉) rExpSeq) . (((2 * k) + 1) + 1)) + (((- c₉) rExpSeq) . (((2 * k) + 1) + 2)) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() even Element of NAT
(2 * k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real positive non negative V70() V71() V72() V73() V74() V75() non even Element of NAT
n + 2 is 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
(Partial_Sums ((- Prob) rExpSeq)) . (n + 2) is V28() real ext-real Element of REAL
(Partial_Sums ((- Prob) rExpSeq)) ^\ 1 is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL , Partial_Sums ((- Prob) rExpSeq))
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (1 - Prob)) . n is V28() real ext-real Element of REAL
((Partial_Sums ((- Prob) rExpSeq)) ^\ 1) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Partial_Sums ((- Prob) rExpSeq)) . (n + 1) is V28() real ext-real Element of REAL
lim (NAT --> (1 - Prob)) is V28() real ext-real Element of REAL
(NAT --> (1 - Prob)) . 1 is V28() real ext-real Element of REAL
lim ((Partial_Sums ((- Prob) rExpSeq)) ^\ 1) is V28() real ext-real Element of REAL
lim (Partial_Sums ((- Prob) rExpSeq)) is V28() real ext-real Element of REAL
Sum ((- Prob) rExpSeq) is V28() real ext-real Element of REAL
Omega is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sigma is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Sigma . Prob is V28() real ext-real set
Omega . Prob is V28() real ext-real set
- (Omega . Prob) is V28() real ext-real set
(- (Omega . Prob)) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum ((- (Omega . Prob)) rExpSeq) is V28() real ext-real Element of REAL
Sigma is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma . A is V28() real ext-real set
Prob . A is V28() real ext-real set
Sigma . A is V28() real ext-real Element of REAL
Omega . A is V28() real ext-real Element of REAL
- (Omega . A) is V28() real ext-real Element of REAL
(- (Omega . A)) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum ((- (Omega . A)) rExpSeq) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
((Prob * A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product ((Prob * A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product ((Prob * A))) . n is V28() real ext-real Element of REAL
(Partial_Sums (Prob * A)) . n is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * A)) . 0 is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * A)) . 0) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . 0)) is V28() real ext-real Element of REAL
(Prob * A) . 0 is V28() real ext-real Element of REAL
- ((Prob * A) . 0) is V28() real ext-real Element of REAL
exp_R . (- ((Prob * A) . 0)) is V28() real ext-real Element of REAL
(Partial_Product ((Prob * A))) . 0 is V28() real ext-real Element of REAL
((Prob * A)) . 0 is V28() real ext-real Element of REAL
(- ((Prob * A) . 0)) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum ((- ((Prob * A) . 0)) rExpSeq) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * A)) . n is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
(Partial_Product ((Prob * A))) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Partial_Sums (Prob * A)) . (n + 1) is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * A)) . (n + 1)) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . (n + 1))) is V28() real ext-real Element of REAL
(Partial_Product ((Prob * A))) . (n + 1) is V28() real ext-real Element of REAL
((Prob * A)) . (n + 1) is V28() real ext-real Element of REAL
((Partial_Product ((Prob * A))) . n) * (((Prob * A)) . (n + 1)) is V28() real ext-real Element of REAL
(Prob * A) . (n + 1) is V28() real ext-real Element of REAL
- ((Prob * A) . (n + 1)) is V28() real ext-real Element of REAL
(- ((Prob * A) . (n + 1))) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum ((- ((Prob * A) . (n + 1))) rExpSeq) is V28() real ext-real Element of REAL
(exp_R . (- ((Partial_Sums (Prob * A)) . n))) * (Sum ((- ((Prob * A) . (n + 1))) rExpSeq)) is V28() real ext-real Element of REAL
exp_R (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
exp_R (- ((Prob * A) . (n + 1))) is V28() real ext-real Element of REAL
exp_R . (- ((Prob * A) . (n + 1))) is V28() real ext-real Element of REAL
(exp_R (- ((Partial_Sums (Prob * A)) . n))) * (exp_R (- ((Prob * A) . (n + 1)))) is V28() real ext-real Element of REAL
(- ((Partial_Sums (Prob * A)) . n)) + (- ((Prob * A) . (n + 1))) is V28() real ext-real Element of REAL
exp_R ((- ((Partial_Sums (Prob * A)) . n)) + (- ((Prob * A) . (n + 1)))) is V28() real ext-real Element of REAL
exp_R . ((- ((Partial_Sums (Prob * A)) . n)) + (- ((Prob * A) . (n + 1)))) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . n) + ((Prob * A) . (n + 1)) is V28() real ext-real Element of REAL
- (((Partial_Sums (Prob * A)) . n) + ((Prob * A) . (n + 1))) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Complement A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
((Prob * A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product ((Prob * A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * (Complement A))) . n is V28() real ext-real Element of REAL
(Partial_Product ((Prob * A))) . n is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement A))) . 0 is V28() real ext-real Element of REAL
(Prob * (Complement A)) . 0 is V28() real ext-real Element of REAL
dom (Prob * (Complement A)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Complement A) . 0 is Event of Sigma
Prob . ((Complement A) . 0) is V28() real ext-real Element of REAL
A . 0 is Event of Sigma
(A . 0) ` is Element of bool Omega
Prob . ((A . 0) `) is V28() real ext-real set
[#] Sigma is Event of Sigma
([#] Sigma) \ (A . 0) is Event of Sigma
Prob . (([#] Sigma) \ (A . 0)) is V28() real ext-real Element of REAL
Prob . (A . 0) is V28() real ext-real Element of REAL
1 - (Prob . (A . 0)) is V28() real ext-real Element of REAL
(Partial_Product ((Prob * A))) . 0 is V28() real ext-real Element of REAL
((Prob * A)) . 0 is V28() real ext-real Element of REAL
(Prob * A) . 0 is V28() real ext-real Element of REAL
- ((Prob * A) . 0) is V28() real ext-real Element of REAL
(- ((Prob * A) . 0)) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum ((- ((Prob * A) . 0)) rExpSeq) is V28() real ext-real Element of REAL
exp_R . (- ((Prob * A) . 0)) is V28() real ext-real Element of REAL
dom (Prob * A) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
- (Prob . (A . 0)) is V28() real ext-real Element of REAL
1 + (- (Prob . (A . 0))) is V28() real ext-real Element of REAL
exp_R . (- (Prob . (A . 0))) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * (Complement A))) . n is V28() real ext-real Element of REAL
(Partial_Product ((Prob * A))) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Partial_Product (Prob * (Complement A))) . (n + 1) is V28() real ext-real Element of REAL
(Partial_Product ((Prob * A))) . (n + 1) is V28() real ext-real Element of REAL
(Complement A) . (n + 1) is Event of Sigma
Prob . ((Complement A) . (n + 1)) is V28() real ext-real Element of REAL
A . (n + 1) is Event of Sigma
(A . (n + 1)) ` is Element of bool Omega
Prob . ((A . (n + 1)) `) is V28() real ext-real set
([#] Sigma) \ (A . (n + 1)) is Event of Sigma
Prob . (A . (n + 1)) is V28() real ext-real Element of REAL
1 - (Prob . (A . (n + 1))) is V28() real ext-real Element of REAL
- (Prob . (A . (n + 1))) is V28() real ext-real Element of REAL
1 + (- (Prob . (A . (n + 1)))) is V28() real ext-real Element of REAL
exp_R . (- (Prob . (A . (n + 1)))) is V28() real ext-real Element of REAL
(Prob * (Complement A)) . (n + 1) is V28() real ext-real Element of REAL
((Prob * (Complement A)) . (n + 1)) * ((Partial_Product ((Prob * A))) . n) is V28() real ext-real Element of REAL
(exp_R . (- (Prob . (A . (n + 1))))) * ((Partial_Product ((Prob * A))) . n) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Prob * A)) . k is V28() real ext-real Element of REAL
(Prob * A) . k is V28() real ext-real Element of REAL
- ((Prob * A) . k) is V28() real ext-real Element of REAL
exp_R . (- ((Prob * A) . k)) is V28() real ext-real Element of REAL
(- ((Prob * A) . k)) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum ((- ((Prob * A) . k)) rExpSeq) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement A))) . n) * ((Prob * (Complement A)) . (n + 1)) is V28() real ext-real Element of REAL
((Partial_Product ((Prob * A))) . n) * ((Prob * (Complement A)) . (n + 1)) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Complement A)) . k is V28() real ext-real Element of REAL
(Complement A) . k is Event of Sigma
Prob . ((Complement A) . k) is V28() real ext-real Element of REAL
(- (Prob . (A . (n + 1)))) rExpSeq is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum ((- (Prob . (A . (n + 1)))) rExpSeq) is V28() real ext-real Element of REAL
(Sum ((- (Prob . (A . (n + 1)))) rExpSeq)) * ((Partial_Product ((Prob * A))) . n) is V28() real ext-real Element of REAL
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Sums (Prob * A)) . n is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
(Sum ((- (Prob . (A . (n + 1)))) rExpSeq)) * (exp_R . (- ((Partial_Sums (Prob * A)) . n))) is V28() real ext-real Element of REAL
exp_R (- (Prob . (A . (n + 1)))) is V28() real ext-real Element of REAL
exp_R . (- (Prob . (A . (n + 1)))) is V28() real ext-real Element of REAL
exp_R (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
(exp_R (- (Prob . (A . (n + 1))))) * (exp_R (- ((Partial_Sums (Prob * A)) . n))) is V28() real ext-real Element of REAL
(- (Prob . (A . (n + 1)))) + (- ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
exp_R ((- (Prob . (A . (n + 1)))) + (- ((Partial_Sums (Prob * A)) . n))) is V28() real ext-real Element of REAL
exp_R . ((- (Prob . (A . (n + 1)))) + (- ((Partial_Sums (Prob * A)) . n))) is V28() real ext-real Element of REAL
(Prob * A) . (n + 1) is V28() real ext-real Element of REAL
((Prob * A) . (n + 1)) + ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
- (((Prob * A) . (n + 1)) + ((Partial_Sums (Prob * A)) . n)) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * A)) . (n + 1) is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * A)) . (n + 1)) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * A)) . (n + 1))) is V28() real ext-real Element of REAL
bool [:NAT,NAT:] is non empty V94() set
Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Prob is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
A . n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Prob . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,Omega,(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Sigma . Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob + Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Prob is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma . A is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Prob . A is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Sigma . A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A + Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Sigma is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Prob is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma . A is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Prob . A is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Sigma . A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,A,Omega,0,1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega + 1 is 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
Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Prob is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
A . n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Prob . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Prob is set
dom (Omega,Sigma) is non empty V70() V71() V72() V73() V74() V75() set
A is set
(Omega,Sigma) . Prob is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Omega,Sigma) . A is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
dom (Omega,Sigma) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,Omega,(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,Omega,(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Prob is set
dom (Omega,Sigma) is non empty V70() V71() V72() V73() V74() V75() set
A is set
(Omega,Sigma) . Prob is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Omega,Sigma) . A is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
dom (Omega,Sigma) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega + 1 is 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
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega + 1 is 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
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega + 1) + Sigma is 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
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega + 1 is 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
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega + 1) + Sigma is 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
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega + 1 is 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
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Sigma) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,n,(Omega + 1),(n + Sigma),n) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega + 1 is 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
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega) is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
Sigma is set
dom (Omega) is non empty V70() V71() V72() V73() V74() V75() set
Prob is set
(Omega) . Sigma is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Omega) . Prob is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
dom (Omega) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega) . n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A + Omega is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
A is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ Prob is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A - n is V28() real ext-real Element of REAL
(A - n) - 1 is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n,n) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n + n) + 1 is 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
B2 is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k * (n,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * B2 is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * B2) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * B2)) . A is V28() real ext-real Element of REAL
Prob * k is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * k)) . n is V28() real ext-real Element of REAL
k ^\ ((n + n) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),k)
Prob * (k ^\ ((n + n) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (k ^\ ((n + n) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((A - n) - 1) is V28() real ext-real set
((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((A - n) - 1)) is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * B2)) . c₉ is V28() real ext-real Element of REAL
(Partial_Product (Prob * k)) . c₉ is V28() real ext-real Element of REAL
(n) is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(n) . 0 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
0 * ((n) . 0) is empty Relation-like non-empty empty-yielding RAT -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() set
(Partial_Product (Prob * B2)) . (0 * ((n) . 0)) is V28() real ext-real set
(Partial_Product (Prob * k)) . (0 * ((n) . 0)) is V28() real ext-real set
(Partial_Product (Prob * B2)) . 0 is V28() real ext-real Element of REAL
(Prob * B2) . 0 is V28() real ext-real Element of REAL
(Partial_Product (Prob * k)) . 0 is V28() real ext-real Element of REAL
(Prob * k) . 0 is V28() real ext-real Element of REAL
dom (Prob * B2) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
B2 . 0 is Event of Sigma
Prob . (B2 . 0) is V28() real ext-real Element of REAL
dom (k * (n,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(n,n) . 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
0 + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,0,n,(0 + n),0) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k . 0 is Event of Sigma
Prob . (k . 0) is V28() real ext-real Element of REAL
dom (Prob * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n) . k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
k * ((n) . k) is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Partial_Product (Prob * B2)) . (k * ((n) . k)) is V28() real ext-real set
(Partial_Product (Prob * k)) . (k * ((n) . k)) is V28() real ext-real set
k + 1 is 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
(n) . (k + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(k + 1) * ((n) . (k + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Partial_Product (Prob * B2)) . ((k + 1) * ((n) . (k + 1))) is V28() real ext-real set
(Partial_Product (Prob * k)) . ((k + 1) * ((n) . (k + 1))) is V28() real ext-real set
(n) . k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,k,n,0,1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n) . (k + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,(k + 1),n,0,1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * B2) . (k + 1) is V28() real ext-real Element of REAL
(Prob * k) . (k + 1) is V28() real ext-real Element of REAL
dom (Prob * B2) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
B2 . (k + 1) is Event of Sigma
Prob . (B2 . (k + 1)) is V28() real ext-real Element of REAL
dom (k * (n,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(n,n) . (k + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k + 1) + n is 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
(NAT,(k + 1),n,((k + 1) + n),(k + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k . (k + 1) is Event of Sigma
Prob . (k . (k + 1)) is V28() real ext-real Element of REAL
dom (Prob * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Partial_Product (Prob * B2)) . (k + 1) is V28() real ext-real Element of REAL
(Partial_Product (Prob * k)) . k is V28() real ext-real Element of REAL
((Partial_Product (Prob * k)) . k) * ((Prob * k) . (k + 1)) is V28() real ext-real Element of REAL
(n) . (k + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,(k + 1),n,0,1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * B2) . 0 is V28() real ext-real Element of REAL
(Prob * k) . 0 is V28() real ext-real Element of REAL
dom (Prob * B2) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
B2 . 0 is Event of Sigma
Prob . (B2 . 0) is V28() real ext-real Element of REAL
dom (k * (n,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(n,n) . 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
0 + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,0,n,(0 + n),0) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k . 0 is Event of Sigma
Prob . (k . 0) is V28() real ext-real Element of REAL
dom (Prob * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(k + 1) * ((n) . (k + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * B2)) . ((k + 1) * ((n) . (k + 1))) is V28() real ext-real Element of REAL
(Partial_Product (Prob * k)) . ((k + 1) * ((n) . (k + 1))) is V28() real ext-real Element of REAL
(n) . c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,c₉,n,0,1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ * ((n) . c₉) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
0 + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(0 + n) + 1 is 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
(Partial_Product (Prob * B2)) . ((0 + n) + 1) is V28() real ext-real Element of REAL
(Partial_Product (Prob * B2)) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Prob * B2) . (n + 1) is V28() real ext-real Element of REAL
((Partial_Product (Prob * B2)) . n) * ((Prob * B2) . (n + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * k)) . n) * ((Prob * B2) . (n + 1)) is V28() real ext-real Element of REAL
dom (k * (n,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(n,n) . (n + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n + 1) + n is 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
(NAT,(n + 1),n,((n + 1) + n),(n + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 . (n + 1) is Event of Sigma
Prob . (B2 . (n + 1)) is V28() real ext-real Element of REAL
k . ((n + 1) + n) is Event of Sigma
Prob . (k . ((n + 1) + n)) is V28() real ext-real Element of REAL
((n + n) + 1) + 0 is 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
k . (((n + n) + 1) + 0) is Event of Sigma
(k ^\ ((n + n) + 1)) . 0 is Event of Sigma
dom (Prob * (k ^\ ((n + n) + 1))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (k ^\ ((n + n) + 1))) . 0 is V28() real ext-real Element of REAL
dom (Prob * B2) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
((0 + n) + 1) - n is V28() real ext-real Element of REAL
(((0 + n) + 1) - n) - 1 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((((0 + n) + 1) - n) - 1) is V28() real ext-real set
((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((((0 + n) + 1) - n) - 1)) is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(c₉ + n) + 1 is 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
(Partial_Product (Prob * B2)) . ((c₉ + n) + 1) is V28() real ext-real Element of REAL
((c₉ + n) + 1) - n is V28() real ext-real Element of REAL
(((c₉ + n) + 1) - n) - 1 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((((c₉ + n) + 1) - n) - 1) is V28() real ext-real set
((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((((c₉ + n) + 1) - n) - 1)) is V28() real ext-real Element of REAL
c₉ + 1 is 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
(c₉ + 1) + n is 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
((c₉ + 1) + n) + 1 is 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
(Partial_Product (Prob * B2)) . (((c₉ + 1) + n) + 1) is V28() real ext-real Element of REAL
(((c₉ + 1) + n) + 1) - n is V28() real ext-real Element of REAL
((((c₉ + 1) + n) + 1) - n) - 1 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . (((((c₉ + 1) + n) + 1) - n) - 1) is V28() real ext-real set
((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . (((((c₉ + 1) + n) + 1) - n) - 1)) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . c₉ is V28() real ext-real Element of REAL
((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . c₉) is V28() real ext-real Element of REAL
(Prob * B2) . (((c₉ + 1) + n) + 1) is V28() real ext-real Element of REAL
(((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . c₉)) * ((Prob * B2) . (((c₉ + 1) + n) + 1)) is V28() real ext-real Element of REAL
(Prob * (k ^\ ((n + n) + 1))) . (c₉ + 1) is V28() real ext-real Element of REAL
(c₉ + 1) + 1 is 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
n + ((c₉ + 1) + 1) is 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
(n,n) . (((c₉ + 1) + n) + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(((c₉ + 1) + n) + 1) + n is 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
(NAT,(((c₉ + 1) + n) + 1),n,((((c₉ + 1) + n) + 1) + n),(((c₉ + 1) + n) + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 . (((c₉ + 1) + n) + 1) is Event of Sigma
((n + n) + 1) + (c₉ + 1) is 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
k . (((n + n) + 1) + (c₉ + 1)) is Event of Sigma
Prob . (B2 . (((c₉ + 1) + n) + 1)) is V28() real ext-real Element of REAL
(k ^\ ((n + n) + 1)) . (c₉ + 1) is Event of Sigma
Prob . ((k ^\ ((n + n) + 1)) . (c₉ + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . c₉) * ((Prob * (k ^\ ((n + n) + 1))) . (c₉ + 1)) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . (c₉ + 1) is V28() real ext-real Element of REAL
(n + 1) - 1 is V28() real ext-real Element of REAL
A - 1 is V28() real ext-real Element of REAL
(A - 1) - n is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((A - n) - 1) + n is V28() real ext-real Element of REAL
(((A - n) - 1) + n) + 1 is V28() real ext-real Element of REAL
((((A - n) - 1) + n) + 1) - n is V28() real ext-real Element of REAL
(((((A - n) - 1) + n) + 1) - n) - 1 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((((((A - n) - 1) + n) + 1) - n) - 1) is V28() real ext-real set
((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((((((A - n) - 1) + n) + 1) - n) - 1)) is V28() real ext-real Element of REAL
c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
B2 is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection B2 is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k,r) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
c₉ * (k,r) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection B2) . n is Event of Sigma
(Partial_Intersection c₉) . k is Event of Sigma
k + r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k + r) + 1 is 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
c₉ ^\ ((k + r) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),c₉)
Partial_Intersection (c₉ ^\ ((k + r) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n - k is V28() real ext-real Element of REAL
(n - k) - 1 is V28() real ext-real Element of REAL
(Partial_Intersection (c₉ ^\ ((k + r) + 1))) . ((n - k) - 1) is set
((Partial_Intersection c₉) . k) /\ ((Partial_Intersection (c₉ ^\ ((k + r) + 1))) . ((n - k) - 1)) is Element of bool Omega
m is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
k * m is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
s is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection s is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection s) . k is Event of Sigma
m is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
c₉ . z is set
q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
s . q is Event of Sigma
dom (c₉ * (k,r)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(k,r) . q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
q + r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,q,k,(q + r),q) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ . q is Event of Sigma
dom (c₉ * (k,r)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(k,r) . q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
q + r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,q,k,(q + r),q) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
q is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . q is set
m is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
z + ((k + r) + 1) is 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
c₉ . (z + ((k + r) + 1)) is Event of Sigma
(c₉ ^\ ((k + r) + 1)) . z is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
k + 1 is 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
z - (k + 1) is V28() real ext-real Element of REAL
z - k is V28() real ext-real Element of REAL
(z - k) - 1 is V28() real ext-real Element of REAL
q is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n - (k + 1) is V28() real ext-real Element of REAL
q + ((k + r) + 1) is 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
c₉ . (q + ((k + r) + 1)) is Event of Sigma
dom (c₉ * (k,r)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k,r) . k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k + r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,k,k,(k + r),k) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
m is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
z - k is V28() real ext-real Element of REAL
(z - k) - 1 is V28() real ext-real Element of REAL
s . z is set
k + 1 is 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
0 + (k + 1) is 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
z - (k + 1) is V28() real ext-real Element of REAL
(z - (k + 1)) + (k + 1) is V28() real ext-real Element of REAL
(k + 1) - 1 is V28() real ext-real Element of REAL
z - 1 is V28() real ext-real Element of REAL
z + 1 is 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
(z + 1) - 1 is V28() real ext-real Element of REAL
n - (k + 1) is V28() real ext-real Element of REAL
(n - (k + 1)) + (k + 1) is V28() real ext-real Element of REAL
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(c₉ ^\ ((k + r) + 1)) . z is set
z + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(z + k) + 1 is 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
((z + k) + 1) - k is V28() real ext-real Element of REAL
(((z + k) + 1) - k) - 1 is V28() real ext-real Element of REAL
s . ((z + k) + 1) is Event of Sigma
dom (c₉ * (k,r)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
k + 1 is 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
(k + 1) + z is 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
(k,r) . ((z + k) + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((z + k) + 1) + r is 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
(NAT,((z + k) + 1),k,(((z + k) + 1) + r),((z + k) + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((k + r) + 1) + z is 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
c₉ . (((k + r) + 1) + z) is Event of Sigma
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(c₉ ^\ ((k + r) + 1)) . z is set
(Partial_Intersection s) . n is Event of Sigma
m is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
q is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . q is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . k is set
m is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
q is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . q is set
m is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
z is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
s . z is set
B2 is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k * (n,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * B2 is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * B2) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * B2)) . A is V28() real ext-real Element of REAL
Prob * k is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * k)) . n is V28() real ext-real Element of REAL
k ^\ ((n + n) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),k)
Prob * (k ^\ ((n + n) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (k ^\ ((n + n) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((A - n) - 1) is V28() real ext-real set
((Partial_Product (Prob * k)) . n) * ((Partial_Product (Prob * (k ^\ ((n + n) + 1)))) . ((A - n) - 1)) is V28() real ext-real Element of REAL
r is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
c₉ * n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
r * (n,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection k) . A is Event of Sigma
Partial_Intersection r is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection r) . n is Event of Sigma
r ^\ ((n + n) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),r)
Partial_Intersection (r ^\ ((n + n) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (r ^\ ((n + n) + 1))) . ((A - n) - 1) is set
((Partial_Intersection r) . n) /\ ((Partial_Intersection (r ^\ ((n + n) + 1))) . ((A - n) - 1)) is Element of bool Omega
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Complement A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (Complement A)) . n is Event of Sigma
n - n is V28() real ext-real Element of REAL
(n - n) - 1 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement A))) . n is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n + k) + 1 is 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
A ^\ ((n + k) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Partial_Intersection (A ^\ ((n + k) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (A ^\ ((n + k) + 1))) . ((n - n) - 1) is set
((Partial_Intersection (Complement A)) . n) /\ ((Partial_Intersection (A ^\ ((n + k) + 1))) . ((n - n) - 1)) is Element of bool Omega
Prob . (((Partial_Intersection (Complement A)) . n) /\ ((Partial_Intersection (A ^\ ((n + k) + 1))) . ((n - n) - 1))) is V28() real ext-real set
Prob * (A ^\ ((n + k) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (A ^\ ((n + k) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (A ^\ ((n + k) + 1)))) . ((n - n) - 1) is V28() real ext-real set
((Partial_Product (Prob * (Complement A))) . n) * ((Partial_Product (Prob * (A ^\ ((n + k) + 1)))) . ((n - n) - 1)) is V28() real ext-real Element of REAL
c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
B2 is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * c₉ is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * c₉) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
B2 * (k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
B2 ^\ k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),B2)
Prob * (B2 ^\ k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (B2 ^\ k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * (B2 ^\ k))) . r is V28() real ext-real Element of REAL
(Partial_Product (Prob * c₉)) . r is V28() real ext-real Element of REAL
dom (Prob * (B2 ^\ k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (B2 ^\ k)) . 0 is V28() real ext-real Element of REAL
(B2 ^\ k) . 0 is Event of Sigma
Prob . ((B2 ^\ k) . 0) is V28() real ext-real Element of REAL
0 + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 . (0 + k) is Event of Sigma
Prob . (B2 . (0 + k)) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (B2 ^\ k))) . 0 is V28() real ext-real Element of REAL
B2 . k is Event of Sigma
Prob . (B2 . k) is V28() real ext-real Element of REAL
(Partial_Product (Prob * c₉)) . 0 is V28() real ext-real Element of REAL
(Prob * c₉) . 0 is V28() real ext-real Element of REAL
(k) . 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
dom (B2 * (k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
c₉ . 0 is Event of Sigma
Prob . (c₉ . 0) is V28() real ext-real Element of REAL
dom (Prob * c₉) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * (B2 ^\ k))) . n is V28() real ext-real Element of REAL
(Partial_Product (Prob * c₉)) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Partial_Product (Prob * (B2 ^\ k))) . (n + 1) is V28() real ext-real Element of REAL
(Partial_Product (Prob * c₉)) . (n + 1) is V28() real ext-real Element of REAL
(Prob * (B2 ^\ k)) . (n + 1) is V28() real ext-real Element of REAL
((Partial_Product (Prob * c₉)) . n) * ((Prob * (B2 ^\ k)) . (n + 1)) is V28() real ext-real Element of REAL
(Prob * c₉) . (n + 1) is V28() real ext-real Element of REAL
(B2 ^\ k) . (n + 1) is Event of Sigma
Prob . ((B2 ^\ k) . (n + 1)) is V28() real ext-real Element of REAL
c₉ . (n + 1) is Event of Sigma
Prob . (c₉ . (n + 1)) is V28() real ext-real Element of REAL
(k) . (n + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 . ((k) . (n + 1)) is Event of Sigma
(n + 1) + k is 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
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(c₉,k) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
c₉ + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(c₉ + k) + 1 is 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
B2 - c₉ is V28() real ext-real Element of REAL
(B2 - c₉) - 1 is V28() real ext-real Element of REAL
r is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A * r is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
m is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n * (c₉,k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection m is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection m) . B2 is Event of Sigma
Prob . ((Partial_Intersection m) . B2) is V28() real ext-real Element of REAL
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * n)) . c₉ is V28() real ext-real Element of REAL
n ^\ ((c₉ + k) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Prob * (n ^\ ((c₉ + k) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (n ^\ ((c₉ + k) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (n ^\ ((c₉ + k) + 1)))) . ((B2 - c₉) - 1) is V28() real ext-real set
((Partial_Product (Prob * n)) . c₉) * ((Partial_Product (Prob * (n ^\ ((c₉ + k) + 1)))) . ((B2 - c₉) - 1)) is V28() real ext-real Element of REAL
r * (c₉,k) is non empty Relation-like NAT -defined NAT -valued RAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(r * (c₉,k)) . s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . ((r * (c₉,k)) . s) is Event of Sigma
m . s is Event of Sigma
(A * r) * (c₉,k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
dom ((A * r) * (c₉,k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(c₉,k) . s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A * r) . ((c₉,k) . s) is Event of Sigma
dom (A * r) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
r . ((c₉,k) . s) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (r . ((c₉,k) . s)) is Event of Sigma
dom (r * (c₉,k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(r * (c₉,k)) . s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . ((r * (c₉,k)) . s) is Event of Sigma
m . s is Event of Sigma
Prob * m is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * m) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * m)) . B2 is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(c₉) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A * k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
r is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
r * (c₉) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection n) . B2 is Event of Sigma
Prob . ((Partial_Intersection n) . B2) is V28() real ext-real Element of REAL
r ^\ c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),r)
Prob * (r ^\ c₉) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (r ^\ c₉)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (r ^\ c₉))) . B2 is V28() real ext-real Element of REAL
k * (c₉) is non empty Relation-like NAT -defined NAT -valued RAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
dom (k * (c₉)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k * (c₉)) . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . ((k * (c₉)) . m) is Event of Sigma
n . m is Event of Sigma
A * (k * (c₉)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
dom (A * (k * (c₉))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(A * (k * (c₉))) . m is Event of Sigma
dom (A * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(c₉) . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A * k) . ((c₉) . m) is Event of Sigma
k . ((c₉) . m) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (k . ((c₉) . m)) is Event of Sigma
(A * k) * (c₉) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
dom ((A * k) * (c₉)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k * (c₉)) . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . ((k * (c₉)) . m) is Event of Sigma
n . m is Event of Sigma
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * n)) . B2 is V28() real ext-real Element of REAL
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (A ^\ ((n + k) + 1))) . B2 is Event of Sigma
((Partial_Intersection (Complement A)) . n) /\ ((Partial_Intersection (A ^\ ((n + k) + 1))) . B2) is Event of Sigma
Prob . (((Partial_Intersection (Complement A)) . n) /\ ((Partial_Intersection (A ^\ ((n + k) + 1))) . B2)) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (A ^\ ((n + k) + 1)))) . B2 is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement A))) . n) * ((Partial_Product (Prob * (A ^\ ((n + k) + 1)))) . B2) is V28() real ext-real Element of REAL
c₉ is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A * c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
0 + r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(0 + r) + 1 is 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
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (Complement n)) . 0 is Event of Sigma
n ^\ ((0 + r) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Partial_Intersection (n ^\ ((0 + r) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (n ^\ ((0 + r) + 1))) . k is Event of Sigma
((Partial_Intersection (Complement n)) . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is Event of Sigma
Prob . (((Partial_Intersection (Complement n)) . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is V28() real ext-real Element of REAL
Prob * (Complement n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (Complement n))) . 0 is V28() real ext-real Element of REAL
Prob * (n ^\ ((0 + r) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (n ^\ ((0 + r) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement n))) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k) is V28() real ext-real Element of REAL
(Complement n) . 0 is Event of Sigma
((Complement n) . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is Event of Sigma
Prob . (((Complement n) . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is V28() real ext-real Element of REAL
n . 0 is Event of Sigma
(n . 0) ` is Element of bool Omega
((n . 0) `) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is Element of bool Omega
Prob . (((n . 0) `) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is V28() real ext-real set
Omega \ (n . 0) is Element of bool Omega
(Omega \ (n . 0)) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is Element of bool Omega
Prob . ((Omega \ (n . 0)) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is V28() real ext-real set
Omega /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is Element of bool Omega
(n . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is Event of Sigma
(Omega /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) \ ((n . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is Element of bool Omega
Prob . ((Omega /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) \ ((n . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k))) is V28() real ext-real set
((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) \ ((n . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is Event of Sigma
Prob . (((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) \ ((n . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k))) is V28() real ext-real Element of REAL
Prob . ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is V28() real ext-real Element of REAL
Prob . ((n . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is V28() real ext-real Element of REAL
(Prob . ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) - (Prob . ((n . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k))) is V28() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m + 1 is 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
(m + 1) + k is 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
s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(m,m) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n * (m,m) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
z is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
q is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection q is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection q) . s is Event of Sigma
Prob . ((Partial_Intersection q) . s) is V28() real ext-real Element of REAL
Partial_Intersection n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection n) . m is Event of Sigma
m + m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(m + m) + 1 is 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
n ^\ ((m + m) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Partial_Intersection (n ^\ ((m + m) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
s - m is V28() real ext-real Element of REAL
(s - m) - 1 is V28() real ext-real Element of REAL
(Partial_Intersection (n ^\ ((m + m) + 1))) . ((s - m) - 1) is set
((Partial_Intersection n) . m) /\ ((Partial_Intersection (n ^\ ((m + m) + 1))) . ((s - m) - 1)) is Element of bool Omega
Prob . (((Partial_Intersection n) . m) /\ ((Partial_Intersection (n ^\ ((m + m) + 1))) . ((s - m) - 1))) is V28() real ext-real set
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * n)) . 0 is V28() real ext-real Element of REAL
((Partial_Product (Prob * n)) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k) is V28() real ext-real Element of REAL
(Partial_Intersection n) . 0 is Event of Sigma
((Partial_Intersection n) . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k) is Event of Sigma
Prob . (((Partial_Intersection n) . 0) /\ ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) is V28() real ext-real Element of REAL
(Prob . ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) - (((Partial_Product (Prob * n)) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k)) is V28() real ext-real Element of REAL
(Prob * n) . 0 is V28() real ext-real Element of REAL
((Prob * n) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k) is V28() real ext-real Element of REAL
(Prob . ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) - (((Prob * n) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k)) is V28() real ext-real Element of REAL
(Prob * (Complement n)) . 0 is V28() real ext-real Element of REAL
1 - ((Prob * (Complement n)) . 0) is V28() real ext-real Element of REAL
((n . 0) `) ` is Element of bool Omega
Omega \ ((n . 0) `) is Element of bool Omega
Prob . (n . 0) is V28() real ext-real Element of REAL
[#] Sigma is Event of Sigma
([#] Sigma) \ ((n . 0) `) is Element of bool Omega
Prob . (([#] Sigma) \ ((n . 0) `)) is V28() real ext-real set
Prob . ((n . 0) `) is V28() real ext-real set
1 - (Prob . ((n . 0) `)) is V28() real ext-real Element of REAL
dom (Prob * n) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom (Prob * (Complement n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
Prob . ((Complement n) . 0) is V28() real ext-real Element of REAL
((Prob * (Complement n)) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k) - (((Prob * (Complement n)) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k)) is V28() real ext-real Element of REAL
(Prob . ((Partial_Intersection (n ^\ ((0 + r) + 1))) . k)) - (((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k) - (((Prob * (Complement n)) . 0) * ((Partial_Product (Prob * (n ^\ ((0 + r) + 1)))) . k))) is V28() real ext-real Element of REAL
(((0 + r) + 1)) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n * (((0 + r) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
C is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
B is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection B is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
C * (k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
C ^\ k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),C)
Partial_Intersection (C ^\ k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (C ^\ k)) . n is Event of Sigma
(Partial_Intersection B) . n is Event of Sigma
e is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A * e is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
x is set
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
B . knat is set
dom (C * (k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(C * (k)) . knat is Event of Sigma
(k) . knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
C . ((k) . knat) is Event of Sigma
knat + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B . knat is Event of Sigma
(C ^\ k) . knat is Event of Sigma
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(C ^\ k) . knat is set
dom (C * (k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(C * (k)) . knat is Event of Sigma
(k) . knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
C . ((k) . knat) is Event of Sigma
knat + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B . knat is Event of Sigma
(C ^\ k) . knat is Event of Sigma
x is set
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(C ^\ k) . knat is set
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
B . knat is set
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(C ^\ k) . knat is set
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
B . knat is set
B is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection B is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection B) . k is Event of Sigma
Prob . ((Partial_Intersection B) . k) is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ + 1 is 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
k is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A * k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(c₉ + 1) + n is 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
((c₉ + 1) + n) + 1 is 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
r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement m is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement m) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (Complement m)) . (c₉ + 1) is Event of Sigma
m ^\ (((c₉ + 1) + n) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),m)
Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r is Event of Sigma
((Partial_Intersection (Complement m)) . (c₉ + 1)) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r) is Event of Sigma
Prob . (((Partial_Intersection (Complement m)) . (c₉ + 1)) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) is V28() real ext-real Element of REAL
Prob * (Complement m) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement m)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (Complement m))) . (c₉ + 1) is V28() real ext-real Element of REAL
Prob * (m ^\ (((c₉ + 1) + n) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1)))) . r is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . (c₉ + 1)) * ((Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1)))) . r) is V28() real ext-real Element of REAL
(Partial_Intersection (Complement m)) . c₉ is Event of Sigma
(Complement m) . (c₉ + 1) is Event of Sigma
((Partial_Intersection (Complement m)) . c₉) /\ ((Complement m) . (c₉ + 1)) is Event of Sigma
(((Partial_Intersection (Complement m)) . c₉) /\ ((Complement m) . (c₉ + 1))) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r) is Event of Sigma
Prob . ((((Partial_Intersection (Complement m)) . c₉) /\ ((Complement m) . (c₉ + 1))) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) is V28() real ext-real Element of REAL
m . (c₉ + 1) is Event of Sigma
(m . (c₉ + 1)) ` is Element of bool Omega
((m . (c<sub>9</sub> + 1)) `) /\ ((Partial_Intersection (Complement m)) . c₉) is Element of bool Omega
(((m . (c₉ + 1)) `) /\ ((Partial_Intersection (Complement m)) . c<sub>9</sub>)) /\ ((Partial_Intersection (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . r) is Element of bool Omega
Prob . ((((m . (c<sub>9</sub> + 1)) `) /\ ((Partial_Intersection (Complement m)) . c₉)) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) is V28() real ext-real set
((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r) is Event of Sigma
((m . (c₉ + 1)) `) /\ (((Partial_Intersection (Complement m)) . c<sub>9</sub>) /\ ((Partial_Intersection (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . r)) is Element of bool Omega
Prob . (((m . (c<sub>9</sub> + 1)) `) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r))) is V28() real ext-real set
Omega \ (m . (c₉ + 1)) is Element of bool Omega
(Omega \ (m . (c₉ + 1))) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) is Element of bool Omega
Prob . ((Omega \ (m . (c₉ + 1))) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r))) is V28() real ext-real set
Omega /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) is Element of bool Omega
(m . (c₉ + 1)) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) is Event of Sigma
(Omega /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r))) \ ((m . (c₉ + 1)) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r))) is Element of bool Omega
Prob . ((Omega /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r))) \ ((m . (c₉ + 1)) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)))) is V28() real ext-real set
(((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) \ ((m . (c₉ + 1)) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r))) is Event of Sigma
Prob . ((((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) \ ((m . (c₉ + 1)) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)))) is V28() real ext-real Element of REAL
Prob . (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r)) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement m))) . c₉ is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . c₉) * ((Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1)))) . r) is V28() real ext-real Element of REAL
1 + n is 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
c₉ + (1 + n) is 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
(c₉ + (1 + n)) + 1 is 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
m ^\ ((c₉ + (1 + n)) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),m)
Prob * (m ^\ ((c₉ + (1 + n)) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (m ^\ ((c₉ + (1 + n)) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (m ^\ ((c₉ + (1 + n)) + 1)))) . r is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . c₉) * ((Partial_Product (Prob * (m ^\ ((c₉ + (1 + n)) + 1)))) . r) is V28() real ext-real Element of REAL
Prob * m is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Prob * m) . (c₉ + 1) is V28() real ext-real Element of REAL
((Prob * m) . (c₉ + 1)) * ((Partial_Product (Prob * (Complement m))) . c₉) is V28() real ext-real Element of REAL
(((Prob * m) . (c₉ + 1)) * ((Partial_Product (Prob * (Complement m))) . c₉)) * ((Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1)))) . r) is V28() real ext-real Element of REAL
(((Partial_Product (Prob * (Complement m))) . c₉) * ((Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1)))) . r)) - ((((Prob * m) . (c₉ + 1)) * ((Partial_Product (Prob * (Complement m))) . c₉)) * ((Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1)))) . r)) is V28() real ext-real Element of REAL
Prob . ((m . (c₉ + 1)) /\ (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ (((c₉ + 1) + n) + 1))) . r))) is V28() real ext-real Element of REAL
(c₉,n) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
m * (c₉,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
s is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
s . m is Element of K496(Omega)
dom (m * (c₉,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(c₉,n) . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . ((c₉,n) . m) is Event of Sigma
k * (c₉,n) is non empty Relation-like NAT -defined NAT -valued RAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
dom (k * (c₉,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
z is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
dom z is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
m is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
A * z is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
q is set
m . q is set
(A * z) . q is set
dom (A * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(c₉,n) . k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A * k) . ((c₉,n) . k) is Event of Sigma
k . ((c₉,n) . k) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (k . ((c₉,n) . k)) is Event of Sigma
(A * k) * (c₉,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
dom ((A * k) * (c₉,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
((A * k) * (c₉,n)) . k is Event of Sigma
(k * (c₉,n)) . k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . ((k * (c₉,n)) . k) is Event of Sigma
dom (A * z) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
Complement m is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement m) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (Complement m)) . c₉ is Event of Sigma
c₉ + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(c₉ + 0) + 1 is 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
m ^\ ((c₉ + 0) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),m)
Partial_Intersection (m ^\ ((c₉ + 0) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
r + 1 is 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
(Partial_Intersection (m ^\ ((c₉ + 0) + 1))) . (r + 1) is Event of Sigma
((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ ((c₉ + 0) + 1))) . (r + 1)) is Event of Sigma
Prob . (((Partial_Intersection (Complement m)) . c₉) /\ ((Partial_Intersection (m ^\ ((c₉ + 0) + 1))) . (r + 1))) is V28() real ext-real Element of REAL
Prob * (Complement m) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement m)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (Complement m))) . c₉ is V28() real ext-real Element of REAL
Prob * (m ^\ ((c₉ + 0) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (m ^\ ((c₉ + 0) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (m ^\ ((c₉ + 0) + 1)))) . (r + 1) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . c₉) * ((Partial_Product (Prob * (m ^\ ((c₉ + 0) + 1)))) . (r + 1)) is V28() real ext-real Element of REAL
q is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement m) . k is set
(Complement m) . k is set
dom (m * (c₉,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(m * (c₉,n)) . knat is Event of Sigma
(c₉,n) . knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . ((c₉,n) . knat) is Event of Sigma
knat + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,knat,(c₉ + 1),(knat + n),knat) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement m) . knat is Event of Sigma
m . knat is Event of Sigma
(m . knat) ` is Element of bool Omega
q is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement m) . k is set
(Complement m) . k is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement m) . k is set
(Complement m) . k is set
q is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement m) . k is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement m) . k is set
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement m) . knat is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement m) . k is set
m ^\ (c<sub>9</sub> + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),m)
Partial_Intersection (m ^\ (c<sub>9</sub> + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (m ^\ (c<sub>9</sub> + 1))) . (r + 1) is Event of Sigma
(m . (c<sub>9</sub> + 1)) /\ ((Partial_Intersection (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . r) is Event of Sigma
(c<sub>9</sub> + 1) + 1 is 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
m ^\ ((c<sub>9</sub> + 1) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),m)
q is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(m ^\ ((c<sub>9</sub> + 1) + 1)) . k is set
(m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . k is set
dom (m * (c<sub>9</sub>,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
knat + c<sub>9</sub> is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(knat + c<sub>9</sub>) + 1 is 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
((knat + c<sub>9</sub>) + 1) + 1 is 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
c<sub>9</sub> + 2 is 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
(c<sub>9</sub> + 2) + knat is 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
(c<sub>9</sub>,n) . (((knat + c<sub>9</sub>) + 1) + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(((knat + c<sub>9</sub>) + 1) + 1) + n is 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
(NAT,(((knat + c<sub>9</sub>) + 1) + 1),(c<sub>9</sub> + 1),((((knat + c<sub>9</sub>) + 1) + 1) + n),(((knat + c<sub>9</sub>) + 1) + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
knat + ((c<sub>9</sub> + 1) + 1) is 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
m . (knat + ((c<sub>9</sub> + 1) + 1)) is Event of Sigma
knat + (((c<sub>9</sub> + 1) + n) + 1) is 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
m . (knat + (((c<sub>9</sub> + 1) + n) + 1)) is Event of Sigma
(m ^\ ((c<sub>9</sub> + 1) + 1)) . knat is Event of Sigma
q is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(m ^\ ((c<sub>9</sub> + 1) + 1)) . k is set
(m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . k is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . k is set
(m ^\ ((c<sub>9</sub> + 1) + 1)) . k is set
Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . r is Event of Sigma
q is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . k is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(m ^\ ((c<sub>9</sub> + 1) + 1)) . k is set
knat is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . knat is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(m ^\ ((c<sub>9</sub> + 1) + 1)) . k is set
((Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . r) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
(Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . 0 is Event of Sigma
((Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . 0) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
0 + 1 is 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
(Partial_Intersection (m ^\ (c<sub>9</sub> + 1))) . (0 + 1) is Event of Sigma
(m ^\ ((c<sub>9</sub> + 1) + 1)) . 0 is Event of Sigma
((m ^\ ((c<sub>9</sub> + 1) + 1)) . 0) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
0 + ((c<sub>9</sub> + 1) + 1) is 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
m . (0 + ((c<sub>9</sub> + 1) + 1)) is Event of Sigma
(m . (0 + ((c<sub>9</sub> + 1) + 1))) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
(m ^\ (c<sub>9</sub> + 1)) . (0 + 1) is Event of Sigma
((m ^\ (c<sub>9</sub> + 1)) . (0 + 1)) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
dom (m * (c<sub>9</sub>,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(c<sub>9</sub>,n) . (c<sub>9</sub> + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,(c<sub>9</sub> + 1),(c<sub>9</sub> + 1),((c<sub>9</sub> + 1) + n),(c<sub>9</sub> + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
0 + (c<sub>9</sub> + 1) is 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
m . (0 + (c<sub>9</sub> + 1)) is Event of Sigma
((m ^\ (c<sub>9</sub> + 1)) . (0 + 1)) /\ (m . (0 + (c<sub>9</sub> + 1))) is Event of Sigma
(m ^\ (c<sub>9</sub> + 1)) . 0 is Event of Sigma
((m ^\ (c<sub>9</sub> + 1)) . (0 + 1)) /\ ((m ^\ (c<sub>9</sub> + 1)) . 0) is Event of Sigma
(Partial_Intersection (m ^\ (c<sub>9</sub> + 1))) . 0 is Event of Sigma
((Partial_Intersection (m ^\ (c<sub>9</sub> + 1))) . 0) /\ ((m ^\ (c<sub>9</sub> + 1)) . (0 + 1)) is Event of Sigma
q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . q is Event of Sigma
((Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . q) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
q + 1 is 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
(Partial_Intersection (m ^\ (c<sub>9</sub> + 1))) . (q + 1) is Event of Sigma
(Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . (q + 1) is Event of Sigma
((Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . (q + 1)) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
(q + 1) + 1 is 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
(Partial_Intersection (m ^\ (c<sub>9</sub> + 1))) . ((q + 1) + 1) is Event of Sigma
(m ^\ ((c<sub>9</sub> + 1) + 1)) . (q + 1) is Event of Sigma
((Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . q) /\ ((m ^\ ((c<sub>9</sub> + 1) + 1)) . (q + 1)) is Event of Sigma
(((Partial_Intersection (m ^\ ((c<sub>9</sub> + 1) + 1))) . q) /\ ((m ^\ ((c<sub>9</sub> + 1) + 1)) . (q + 1))) /\ (m . (c<sub>9</sub> + 1)) is Event of Sigma
((Partial_Intersection (m ^\ (c<sub>9</sub> + 1))) . (q + 1)) /\ ((m ^\ ((c<sub>9</sub> + 1) + 1)) . (q + 1)) is Event of Sigma
(m ^\ (c<sub>9</sub> + 1)) . ((q + 1) + 1) is Event of Sigma
(q + 1) + ((c<sub>9</sub> + 1) + 1) is 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
m . ((q + 1) + ((c<sub>9</sub> + 1) + 1)) is Event of Sigma
((q + 1) + 1) + (c<sub>9</sub> + 1) is 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
m . (((q + 1) + 1) + (c<sub>9</sub> + 1)) is Event of Sigma
Prob * (m ^\ (c<sub>9</sub> + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (m ^\ (c<sub>9</sub> + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (m ^\ (c<sub>9</sub> + 1)))) . (r + 1) is V28() real ext-real Element of REAL
((Prob * m) . (c<sub>9</sub> + 1)) * ((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . r) is V28() real ext-real Element of REAL
0 + 1 is 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
(Partial_Product (Prob * (m ^\ (c<sub>9</sub> + 1)))) . (0 + 1) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . 0 is V28() real ext-real Element of REAL
((Prob * m) . (c<sub>9</sub> + 1)) * ((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . 0) is V28() real ext-real Element of REAL
(m ^\ (c<sub>9</sub> + 1)) . (0 + 1) is Event of Sigma
(c<sub>9</sub> + 1) + 1 is 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
(m * (c<sub>9</sub>,n)) . ((c<sub>9</sub> + 1) + 1) is Event of Sigma
dom (m * (c<sub>9</sub>,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(c<sub>9</sub>,n) . ((c<sub>9</sub> + 1) + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((c<sub>9</sub> + 1) + 1) + n is 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
(NAT,((c<sub>9</sub> + 1) + 1),(c<sub>9</sub> + 1),(((c<sub>9</sub> + 1) + 1) + n),((c<sub>9</sub> + 1) + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
0 + (((c<sub>9</sub> + 1) + n) + 1) is 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
m . (0 + (((c<sub>9</sub> + 1) + n) + 1)) is Event of Sigma
Prob . ((m ^\ (c<sub>9</sub> + 1)) . (0 + 1)) is V28() real ext-real Element of REAL
(m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . 0 is Event of Sigma
Prob . ((m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . 0) is V28() real ext-real Element of REAL
dom (Prob * (m ^\ (c<sub>9</sub> + 1))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (m ^\ (c<sub>9</sub> + 1))) . (0 + 1) is V28() real ext-real Element of REAL
(Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . 0 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (m ^\ (c<sub>9</sub> + 1)))) . 0 is V28() real ext-real Element of REAL
((Partial_Product (Prob * (m ^\ (c<sub>9</sub> + 1)))) . 0) * ((Prob * (m ^\ (c<sub>9</sub> + 1))) . (0 + 1)) is V28() real ext-real Element of REAL
(Prob * (m ^\ (c<sub>9</sub> + 1))) . 0 is V28() real ext-real Element of REAL
((Prob * (m ^\ (c<sub>9</sub> + 1))) . 0) * ((Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . 0) is V28() real ext-real Element of REAL
(m ^\ (c<sub>9</sub> + 1)) . 0 is Event of Sigma
0 + (c<sub>9</sub> + 1) is 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
m . (0 + (c<sub>9</sub> + 1)) is Event of Sigma
m . (c<sub>9</sub> + 1) is Event of Sigma
(c<sub>9</sub>,n) . (c<sub>9</sub> + 1) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . ((c<sub>9</sub>,n) . (c<sub>9</sub> + 1)) is Event of Sigma
(NAT,(c<sub>9</sub> + 1),(c<sub>9</sub> + 1),((c<sub>9</sub> + 1) + n),(c<sub>9</sub> + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
dom (Prob * m) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
Prob . ((m ^\ (c<sub>9</sub> + 1)) . 0) is V28() real ext-real Element of REAL
((Prob * m) . (c<sub>9</sub> + 1)) * ((Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . 0) is V28() real ext-real Element of REAL
q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
q + 1 is 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
(Partial_Product (Prob * (m ^\ (c<sub>9</sub> + 1)))) . (q + 1) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . q is V28() real ext-real Element of REAL
((Prob * m) . (c<sub>9</sub> + 1)) * ((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . q) is V28() real ext-real Element of REAL
(q + 1) + 1 is 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
(Partial_Product (Prob * (m ^\ (c<sub>9</sub> + 1)))) . ((q + 1) + 1) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . (q + 1) is V28() real ext-real Element of REAL
((Prob * m) . (c<sub>9</sub> + 1)) * ((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . (q + 1)) is V28() real ext-real Element of REAL
(Prob * (m ^\ (c<sub>9</sub> + 1))) . ((q + 1) + 1) is V28() real ext-real Element of REAL
(Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . (q + 1) is V28() real ext-real Element of REAL
(m ^\ (c<sub>9</sub> + 1)) . ((q + 1) + 1) is Event of Sigma
((q + 1) + 1) + (c<sub>9</sub> + 1) is 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
(m * (c<sub>9</sub>,n)) . (((q + 1) + 1) + (c<sub>9</sub> + 1)) is Event of Sigma
dom (m * (c<sub>9</sub>,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(c<sub>9</sub> + 1) + 1 is 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
((c<sub>9</sub> + 1) + 1) + (q + 1) is 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
(c<sub>9</sub>,n) . (((q + 1) + 1) + (c<sub>9</sub> + 1)) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(((q + 1) + 1) + (c<sub>9</sub> + 1)) + n is 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
(NAT,(((q + 1) + 1) + (c<sub>9</sub> + 1)),(c<sub>9</sub> + 1),((((q + 1) + 1) + (c<sub>9</sub> + 1)) + n),(((q + 1) + 1) + (c<sub>9</sub> + 1))) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(q + 1) + (((c<sub>9</sub> + 1) + n) + 1) is 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
m . ((q + 1) + (((c<sub>9</sub> + 1) + n) + 1)) is Event of Sigma
Prob . ((m ^\ (c<sub>9</sub> + 1)) . ((q + 1) + 1)) is V28() real ext-real Element of REAL
(m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . (q + 1) is Event of Sigma
Prob . ((m ^\ (((c<sub>9</sub> + 1) + n) + 1)) . (q + 1)) is V28() real ext-real Element of REAL
dom (Prob * (m ^\ (c<sub>9</sub> + 1))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(((Prob * m) . (c<sub>9</sub> + 1)) * ((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . q)) * ((Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . (q + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . q) * ((Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . (q + 1)) is V28() real ext-real Element of REAL
((Prob * m) . (c<sub>9</sub> + 1)) * (((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . q) * ((Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . (q + 1))) is V28() real ext-real Element of REAL
dom (m * (c<sub>9</sub>,n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(m * (c<sub>9</sub>,n)) . 0 is Event of Sigma
(c<sub>9</sub>,n) . 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . ((c<sub>9</sub>,n) . 0) is Event of Sigma
0 + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,0,(c<sub>9</sub> + 1),(0 + n),0) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . 0 is Event of Sigma
(m . 0) ` is Element of bool Omega
m . 0 is Event of Sigma
(m . 0) ` is Element of bool Omega
(Complement m) . 0 is Event of Sigma
Prob . ((Complement m) . 0) is V28() real ext-real Element of REAL
(Complement m) . 0 is Event of Sigma
Prob . ((Complement m) . 0) is V28() real ext-real Element of REAL
dom (Prob * (Complement m)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom (Prob * (Complement m)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (Complement m)) . 0 is V28() real ext-real Element of REAL
(Prob * (Complement m)) . 0 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement m))) . 0 is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement m))) . 0 is V28() real ext-real Element of REAL
q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * (Complement m))) . q is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement m))) . q is V28() real ext-real Element of REAL
q + 1 is 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
(Partial_Product (Prob * (Complement m))) . (q + 1) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement m))) . (q + 1) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . k is Event of Sigma
m . k is Event of Sigma
m . (q + 1) is Event of Sigma
(m . (q + 1)) ` is Element of bool Omega
m . (q + 1) is Event of Sigma
(m . (q + 1)) ` is Element of bool Omega
(Complement m) . (q + 1) is Event of Sigma
(Complement m) . (q + 1) is Event of Sigma
Prob . ((Complement m) . (q + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . q) * (Prob . ((Complement m) . (q + 1))) is V28() real ext-real Element of REAL
Prob . ((Complement m) . (q + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . q) * (Prob . ((Complement m) . (q + 1))) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . k is Event of Sigma
m . k is Event of Sigma
knat is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . knat is Event of Sigma
m . knat is Event of Sigma
(Prob * (Complement m)) . (q + 1) is V28() real ext-real Element of REAL
(Prob * (Complement m)) . (q + 1) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . q) * ((Prob * (Complement m)) . (q + 1)) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . k is Event of Sigma
m . k is Event of Sigma
q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m . q is Event of Sigma
m . q is Event of Sigma
(c<sub>9</sub>,n) . q is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
q + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT,q,(c<sub>9</sub> + 1),(q + n),q) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Partial_Intersection (Complement m)) . c<sub>9</sub>) /\ ((m . (c<sub>9</sub> + 1)) /\ ((Partial_Intersection (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . r)) is Event of Sigma
Prob . (((Partial_Intersection (Complement m)) . c<sub>9</sub>) /\ ((m . (c<sub>9</sub> + 1)) /\ ((Partial_Intersection (m ^\ (((c<sub>9</sub> + 1) + n) + 1))) . r))) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement m))) . c<sub>9</sub>) * (((Prob * m) . (c<sub>9</sub> + 1)) * ((Partial_Product (Prob * (m ^\ (((c<sub>9</sub> + 1) + n) + 1)))) . r)) is V28() real ext-real Element of REAL
(Prob * (Complement m)) . (c<sub>9</sub> + 1) is V28() real ext-real Element of REAL
1 - ((Prob * (Complement m)) . (c<sub>9</sub> + 1)) is V28() real ext-real Element of REAL
((m . (c<sub>9</sub> + 1)) `) ` is Element of bool Omega
Omega \ ((m . (c<sub>9</sub> + 1)) `) is Element of bool Omega
Prob . (m . (c₉ + 1)) is V28() real ext-real Element of REAL
[#] Sigma is Event of Sigma
([#] Sigma) \ ((m . (c₉ + 1)) `) is Element of bool Omega
Prob . (([#] Sigma) \ ((m . (c<sub>9</sub> + 1)) `)) is V28() real ext-real set
Prob . ((m . (c₉ + 1)) `) is V28() real ext-real set
1 - (Prob . ((m . (c<sub>9</sub> + 1)) `)) is V28() real ext-real Element of REAL
dom (Prob * m) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom (Prob * (Complement m)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
Prob . ((Complement m) . (c₉ + 1)) is V28() real ext-real Element of REAL
((Prob * (Complement m)) . (c₉ + 1)) * ((Partial_Product (Prob * (Complement m))) . c₉) is V28() real ext-real Element of REAL
(((Prob * (Complement m)) . (c₉ + 1)) * ((Partial_Product (Prob * (Complement m))) . c₉)) * ((Partial_Product (Prob * (m ^\ (((c₉ + 1) + n) + 1)))) . r) is V28() real ext-real Element of REAL
(0) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
dom (0) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
[:NAT,(bool Omega):] is non empty Relation-like set
bool [:NAT,(bool Omega):] is non empty V94() set
A * (0) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is set
(A * (0)) . k is set
A . k is set
(0) . k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
A . ((0) . k) is set
r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(0) . r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
r + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
dom (A * (0)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
k is set
(A * (0)) . k is set
A . k is set
c₉ is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
A * c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
dom c₉ is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n + 1 is 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
(n + 1) - 1 is V28() real ext-real Element of REAL
n - 1 is V28() real ext-real Element of REAL
(n - 1) - n is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement Prob) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Union Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (Complement Prob)) . A is Event of Sigma
(Partial_Union Prob) . A is Event of Sigma
((Partial_Union Prob) . A) ` is Element of bool Omega
n is set
n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
Prob . n is set
(Complement Prob) . n is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement Prob) . k is Event of Sigma
Prob . k is Event of Sigma
(Prob . k) ` is Element of bool Omega
Omega \ (Prob . k) is Element of bool Omega
Omega \ ((Partial_Union Prob) . A) is Element of bool Omega
n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
(Complement Prob) . n is set
Prob . n is set
Omega \ (Prob . n) is Element of bool Omega
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . k is Event of Sigma
(Prob . k) ` is Element of bool Omega
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Union A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (Complement A)) . n is Event of Sigma
Prob . ((Partial_Intersection (Complement A)) . n) is V28() real ext-real Element of REAL
(Partial_Union A) . n is Event of Sigma
Prob . ((Partial_Union A) . n) is V28() real ext-real Element of REAL
1 - (Prob . ((Partial_Union A) . n)) is V28() real ext-real Element of REAL
((Partial_Union A) . n) ` is Element of bool Omega
Prob . (((Partial_Union A) . n) `) is V28() real ext-real set
[#] Sigma is Event of Sigma
([#] Sigma) \ ((Partial_Union A) . n) is Event of Sigma
Prob . (([#] Sigma) \ ((Partial_Union A) . n)) is V28() real ext-real Element of REAL
Omega is set
K496(Omega) is non empty Element of bool (bool Omega)
bool Omega is non empty set
bool (bool Omega) is non empty V94() set
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob is set
K496(Prob) is non empty Element of bool (bool Prob)
bool Prob is non empty set
bool (bool Prob) is non empty V94() set
[:NAT,K496(Prob):] is non empty Relation-like set
bool [:NAT,K496(Prob):] is non empty V94() set
A is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
A ^\ 0 is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ 0) is Element of bool Prob
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is Element of bool Prob
n + 1 is 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
A ^\ (n + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ (n + 1)) is Element of bool Prob
k is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 is Element of bool Prob
c<sub>9</sub> is Element of bool Prob
k + 1 is 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
A ^\ (k + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ (k + 1)) is Element of bool Prob
n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n . 0 is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + 1 is 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
n . (n + 1) is Element of K496(Prob)
A ^\ (n + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ (n + 1)) is Element of bool Prob
n . n is Element of K496(Prob)
c<sub>9</sub> is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is Element of bool Prob
B2 is Element of bool Prob
c<sub>9</sub> + 1 is 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
A ^\ (c<sub>9</sub> + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ (c<sub>9</sub> + 1)) is Element of bool Prob
n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n . 0 is Element of K496(Prob)
n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n . 0 is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n . n is Element of K496(Prob)
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ n) is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
k + 1 is 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
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
k + 1 is 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
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + 1 is 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
n . (B2 + 1) is Element of K496(Prob)
A ^\ (B2 + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ (B2 + 1)) is Element of bool Prob
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . n is Element of K496(Prob)
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ n) is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k + 1 is 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
n . (k + 1) is Element of K496(Prob)
A ^\ (k + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ (k + 1)) is Element of bool Prob
Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . n is Element of K496(Omega)
A . n is Element of K496(Omega)
Sigma ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Sigma)
Union (Sigma ^\ n) is Element of bool Omega
n is set
Prob . n is set
A . n is set
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Prob is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Prob) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Prob) . 0 is Element of K496(Omega)
Prob ^\ 0 is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Prob)
Union (Prob ^\ 0) is Element of bool Omega
(Omega,Prob) . 0 is set
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Prob) . A is set
A + 1 is 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
(Omega,Prob) . (A + 1) is set
(Omega,Prob) . A is Element of K496(Omega)
Prob ^\ (A + 1) is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Prob)
Union (Prob ^\ (A + 1)) is Element of bool Omega
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Prob is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Prob) is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,Prob) is Event of Sigma
Omega is set
K496(Omega) is non empty Element of bool (bool Omega)
bool Omega is non empty set
bool (bool Omega) is non empty V94() set
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob is set
K496(Prob) is non empty Element of bool (bool Prob)
bool Prob is non empty set
bool (bool Prob) is non empty V94() set
[:NAT,K496(Prob):] is non empty Relation-like set
bool [:NAT,K496(Prob):] is non empty V94() set
A is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
A ^\ 0 is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ 0) is Element of bool Prob
Complement (A ^\ 0) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ 0)) is Element of bool Prob
(Union (Complement (A ^\ 0))) ` is Element of bool Prob
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is Element of bool Prob
n + 1 is 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
A ^\ (n + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ (n + 1)) is Element of bool Prob
Complement (A ^\ (n + 1)) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ (n + 1))) is Element of bool Prob
(Union (Complement (A ^\ (n + 1)))) ` is Element of bool Prob
k is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 is Element of bool Prob
c<sub>9</sub> is Element of bool Prob
k + 1 is 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
A ^\ (k + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ (k + 1)) is Element of bool Prob
Complement (A ^\ (k + 1)) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ (k + 1))) is Element of bool Prob
(Union (Complement (A ^\ (k + 1)))) ` is Element of bool Prob
n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n . 0 is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + 1 is 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
n . (n + 1) is Element of K496(Prob)
A ^\ (n + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ (n + 1)) is Element of bool Prob
Complement (A ^\ (n + 1)) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ (n + 1))) is Element of bool Prob
(Union (Complement (A ^\ (n + 1)))) ` is Element of bool Prob
n . n is Element of K496(Prob)
c<sub>9</sub> is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is Element of bool Prob
B2 is Element of bool Prob
c<sub>9</sub> + 1 is 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
A ^\ (c<sub>9</sub> + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ (c<sub>9</sub> + 1)) is Element of bool Prob
Complement (A ^\ (c<sub>9</sub> + 1)) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ (c<sub>9</sub> + 1))) is Element of bool Prob
(Union (Complement (A ^\ (c<sub>9</sub> + 1)))) ` is Element of bool Prob
n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n . 0 is Element of K496(Prob)
n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n . 0 is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n . n is Element of K496(Prob)
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ n) is Element of bool Prob
Complement (A ^\ n) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ n)) is Element of bool Prob
(Union (Complement (A ^\ n))) ` is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
k + 1 is 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
k is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
k + 1 is 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
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + 1 is 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
n . (B2 + 1) is Element of K496(Prob)
A ^\ (B2 + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ (B2 + 1)) is Element of bool Prob
Complement (A ^\ (B2 + 1)) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ (B2 + 1))) is Element of bool Prob
(Union (Complement (A ^\ (B2 + 1)))) ` is Element of bool Prob
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . n is Element of K496(Prob)
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ n) is Element of bool Prob
Complement (A ^\ n) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ n)) is Element of bool Prob
(Union (Complement (A ^\ n))) ` is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k + 1 is 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
n . (k + 1) is Element of K496(Prob)
A ^\ (k + 1) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ (k + 1)) is Element of bool Prob
Complement (A ^\ (k + 1)) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ (k + 1))) is Element of bool Prob
(Union (Complement (A ^\ (k + 1)))) ` is Element of bool Prob
Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . n is Element of K496(Omega)
A . n is Element of K496(Omega)
Sigma ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Sigma)
Intersection (Sigma ^\ n) is Element of bool Omega
Complement (Sigma ^\ n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Sigma ^\ n)) is Element of bool Omega
(Union (Complement (Sigma ^\ n))) ` is Element of bool Omega
n is set
Prob . n is set
A . n is set
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Prob is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Prob) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob ^\ 0 is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Prob)
Complement (Prob ^\ 0) is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Prob ^\ 0)) is Element of bool Omega
(Omega,Prob) . 0 is Element of K496(Omega)
Intersection (Prob ^\ 0) is Element of bool Omega
(Union (Complement (Prob ^\ 0))) ` is Element of bool Omega
(Omega,Prob) . 0 is set
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,Prob) . A is set
A + 1 is 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
(Omega,Prob) . (A + 1) is set
(Omega,Prob) . A is Element of K496(Omega)
Prob ^\ (A + 1) is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Prob)
Complement (Prob ^\ (A + 1)) is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Prob ^\ (A + 1))) is Element of bool Omega
(Omega,Prob) . (A + 1) is Element of K496(Omega)
Intersection (Prob ^\ (A + 1)) is Element of bool Omega
(Union (Complement (Prob ^\ (A + 1)))) ` is Element of bool Omega
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Prob is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Prob) is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,Prob) is Element of bool Omega
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,(Complement Prob)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Prob) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,(Complement Prob)) . A is Event of Sigma
(Omega,Prob) . A is Event of Sigma
((Omega,Prob) . A) ` is Element of bool Omega
n is set
(Complement Prob) ^\ A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega), Complement Prob)
Intersection ((Complement Prob) ^\ A) is Element of bool Omega
Complement ((Complement Prob) ^\ A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement ((Complement Prob) ^\ A)) is Element of bool Omega
(Union (Complement ((Complement Prob) ^\ A))) ` is Element of bool Omega
Prob ^\ A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob ^\ A) . n is Event of Sigma
((Complement Prob) ^\ A) . n is Event of Sigma
A + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement Prob) . (A + n) is Event of Sigma
Prob . (A + n) is Event of Sigma
(Prob . (A + n)) ` is Element of bool Omega
Omega \ (Prob . (A + n)) is Element of bool Omega
Union (Prob ^\ A) is Element of bool Omega
Omega \ ((Omega,Prob) . A) is Element of bool Omega
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Complement Prob) ^\ A) . n is Event of Sigma
(Prob ^\ A) . n is Event of Sigma
A + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . (A + n) is Event of Sigma
Omega \ (Prob . (A + n)) is Element of bool Omega
(Prob . (A + n)) ` is Element of bool Omega
(Complement Prob) . (A + n) is Event of Sigma
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Complement A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (Complement A)) . n is Event of Sigma
Prob . ((Partial_Intersection (Complement A)) . n) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement A))) . n is V28() real ext-real Element of REAL
dom (Prob * (Complement A)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (Complement A)) . 0 is V28() real ext-real Element of REAL
(Complement A) . 0 is Event of Sigma
Prob . ((Complement A) . 0) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement A))) . 0 is V28() real ext-real Element of REAL
(Partial_Intersection (Complement A)) . 0 is Event of Sigma
Prob . ((Partial_Intersection (Complement A)) . 0) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (Complement A)) . n is Event of Sigma
Prob . ((Partial_Intersection (Complement A)) . n) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement A))) . n is V28() real ext-real Element of REAL
n + 1 is 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
(Partial_Intersection (Complement A)) . (n + 1) is Event of Sigma
Prob . ((Partial_Intersection (Complement A)) . (n + 1)) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement A))) . (n + 1) is V28() real ext-real Element of REAL
((Partial_Intersection (Complement A)) . n) /\ ((Partial_Intersection (Complement A)) . n) is Event of Sigma
(Complement A) . (n + 1) is Event of Sigma
(((Partial_Intersection (Complement A)) . n) /\ ((Partial_Intersection (Complement A)) . n)) /\ ((Complement A) . (n + 1)) is Event of Sigma
A . (n + 1) is Event of Sigma
(A . (n + 1)) ` is Element of bool Omega
((Partial_Intersection (Complement A)) . n) /\ ((A . (n + 1)) `) is Element of bool Omega
Omega \ (A . (n + 1)) is Element of bool Omega
((Partial_Intersection (Complement A)) . n) /\ (Omega \ (A . (n + 1))) is Element of bool Omega
((Partial_Intersection (Complement A)) . n) /\ Omega is Element of bool Omega
((Partial_Intersection (Complement A)) . n) /\ (A . (n + 1)) is Event of Sigma
(((Partial_Intersection (Complement A)) . n) /\ Omega) \ (((Partial_Intersection (Complement A)) . n) /\ (A . (n + 1))) is Element of bool Omega
((Partial_Intersection (Complement A)) . n) \ (((Partial_Intersection (Complement A)) . n) /\ (A . (n + 1))) is Event of Sigma
Prob . (((Partial_Intersection (Complement A)) . n) \ (((Partial_Intersection (Complement A)) . n) /\ (A . (n + 1)))) is V28() real ext-real Element of REAL
Prob . (((Partial_Intersection (Complement A)) . n) /\ (A . (n + 1))) is V28() real ext-real Element of REAL
(Prob . ((Partial_Intersection (Complement A)) . n)) - (Prob . (((Partial_Intersection (Complement A)) . n) /\ (A . (n + 1)))) is V28() real ext-real Element of REAL
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Complement k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob * k is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection (Complement k)) . B2 is Event of Sigma
B2 + 1 is 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
k . (B2 + 1) is Event of Sigma
((Partial_Intersection (Complement k)) . B2) /\ (k . (B2 + 1)) is Event of Sigma
Prob . (((Partial_Intersection (Complement k)) . B2) /\ (k . (B2 + 1))) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement k))) . B2 is V28() real ext-real Element of REAL
(Prob * k) . (B2 + 1) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement k))) . B2) * ((Prob * k) . (B2 + 1)) is V28() real ext-real Element of REAL
c<sub>9</sub> is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(B2 + 0) + 1 is 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
k ^\ ((B2 + 0) + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),k)
Partial_Intersection (k ^\ ((B2 + 0) + 1)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
c<sub>9</sub> - B2 is V28() real ext-real Element of REAL
(c<sub>9</sub> - B2) - 1 is V28() real ext-real Element of REAL
(Partial_Intersection (k ^\ ((B2 + 0) + 1))) . ((c<sub>9</sub> - B2) - 1) is set
((Partial_Intersection (Complement k)) . B2) /\ ((Partial_Intersection (k ^\ ((B2 + 0) + 1))) . ((c<sub>9</sub> - B2) - 1)) is Element of bool Omega
Prob . (((Partial_Intersection (Complement k)) . B2) /\ ((Partial_Intersection (k ^\ ((B2 + 0) + 1))) . ((c<sub>9</sub> - B2) - 1))) is V28() real ext-real set
Prob * (k ^\ ((B2 + 0) + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (k ^\ ((B2 + 0) + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (k ^\ ((B2 + 0) + 1)))) . ((c<sub>9</sub> - B2) - 1) is V28() real ext-real set
((Partial_Product (Prob * (Complement k))) . B2) * ((Partial_Product (Prob * (k ^\ ((B2 + 0) + 1)))) . ((c<sub>9</sub> - B2) - 1)) is V28() real ext-real Element of REAL
k ^\ (B2 + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),k)
(k ^\ (B2 + 1)) . 0 is Event of Sigma
((Partial_Intersection (Complement k)) . B2) /\ ((k ^\ (B2 + 1)) . 0) is Event of Sigma
Prob . (((Partial_Intersection (Complement k)) . B2) /\ ((k ^\ (B2 + 1)) . 0)) is V28() real ext-real Element of REAL
Prob * (k ^\ (B2 + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (k ^\ (B2 + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (k ^\ (B2 + 1)))) . 0 is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement k))) . B2) * ((Partial_Product (Prob * (k ^\ (B2 + 1)))) . 0) is V28() real ext-real Element of REAL
0 + (B2 + 1) is 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
k . (0 + (B2 + 1)) is Event of Sigma
(Prob * (k ^\ (B2 + 1))) . 0 is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement k))) . B2) * ((Prob * (k ^\ (B2 + 1))) . 0) is V28() real ext-real Element of REAL
dom (Prob * (k ^\ (B2 + 1))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
Prob . (k . (B2 + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement k))) . B2) * (Prob . (k . (B2 + 1))) is V28() real ext-real Element of REAL
dom (Prob * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Prob * A) . (n + 1) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement A))) . n) * ((Prob * A) . (n + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement A))) . n) - (((Partial_Product (Prob * (Complement A))) . n) * ((Prob * A) . (n + 1))) is V28() real ext-real Element of REAL
((A . (n + 1)) `) ` is Element of bool Omega
Omega \ ((A . (n + 1)) `) is Element of bool Omega
Prob . (A . (n + 1)) is V28() real ext-real Element of REAL
[#] Sigma is Event of Sigma
([#] Sigma) \ ((A . (n + 1)) `) is Element of bool Omega
Prob . (([#] Sigma) \ ((A . (n + 1)) `)) is V28() real ext-real set
Prob . ((A . (n + 1)) `) is V28() real ext-real set
1 - (Prob . ((A . (n + 1)) `)) is V28() real ext-real Element of REAL
dom (Prob * A) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (Complement A)) . (n + 1) is V28() real ext-real Element of REAL
Prob . ((Complement A) . (n + 1)) is V28() real ext-real Element of REAL
1 - ((Prob * (Complement A)) . (n + 1)) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement A))) . n) - ((Partial_Product (Prob * (Complement A))) . n) is V28() real ext-real Element of REAL
((Partial_Product (Prob * (Complement A))) . n) * ((Prob * (Complement A)) . (n + 1)) is V28() real ext-real Element of REAL
(((Partial_Product (Prob * (Complement A))) . n) - ((Partial_Product (Prob * (Complement A))) . n)) + (((Partial_Product (Prob * (Complement A))) . n) * ((Prob * (Complement A)) . (n + 1))) is V28() real ext-real Element of REAL
Omega is set
K496(Omega) is non empty Element of bool (bool Omega)
bool Omega is non empty set
bool (bool Omega) is non empty V94() set
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
superior_setsequence Sigma is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
(Omega,Sigma) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
inferior_setsequence Sigma is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
(Omega,Sigma) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(superior_setsequence Sigma) . Prob is set
(Omega,Sigma) . Prob is set
(superior_setsequence Sigma) . Prob is Element of K496(Omega)
(Omega,Sigma) . Prob is Element of K496(Omega)
A is set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma . (Prob + n) is Element of K496(Omega)
Sigma ^\ Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Sigma)
(Sigma ^\ Prob) . n is Element of K496(Omega)
Union (Sigma ^\ Prob) is Element of bool Omega
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Sigma ^\ Prob) . n is Element of K496(Omega)
Prob + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma . (Prob + n) is Element of K496(Omega)
Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(inferior_setsequence Sigma) . Prob is set
(Omega,Sigma) . Prob is set
(inferior_setsequence Sigma) . Prob is Element of K496(Omega)
(Omega,Sigma) . Prob is Element of K496(Omega)
A is set
Sigma ^\ Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),Sigma)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Sigma ^\ Prob) . n is Element of K496(Omega)
n + Prob is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma . (n + Prob) is Element of K496(Omega)
Intersection (Sigma ^\ Prob) is Element of bool Omega
Complement (Sigma ^\ Prob) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Sigma ^\ Prob)) is Element of bool Omega
(Union (Complement (Sigma ^\ Prob))) ` is Element of bool Omega
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Sigma . (Prob + n) is Element of K496(Omega)
(Sigma ^\ Prob) . n is Element of K496(Omega)
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
A is non empty set
bool A is non empty V94() set
bool (bool A) is non empty V94() set
n is non empty compl-closed sigma-multiplicative Element of bool (bool A)
K496(A) is non empty V94() Element of bool (bool A)
[:NAT,K496(A):] is non empty Relation-like set
bool [:NAT,K496(A):] is non empty V94() set
Prob is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
superior_setsequence Prob is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
(Omega,Prob) is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is non empty Relation-like NAT -defined n -valued K496(A) -valued Function-like V17( NAT ) V18( NAT ,K496(A)) Element of bool [:NAT,K496(A):]
inferior_setsequence n is non empty Relation-like NAT -defined n -valued K496(A) -valued Function-like V17( NAT ) V18( NAT ,K496(A)) non-descending Element of bool [:NAT,K496(A):]
(A,n) is non empty Relation-like NAT -defined n -valued K496(A) -valued Function-like V17( NAT ) V18( NAT ,K496(A)) Element of bool [:NAT,K496(A):]
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
A is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n . n is V28() real ext-real Element of REAL
A ^\ n is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Prob * (A ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum (Prob * (A ^\ n)) is V28() real ext-real Element of REAL
n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . k is V28() real ext-real set
n . k is V28() real ext-real set
n . k is V28() real ext-real Element of REAL
A ^\ k is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Prob * (A ^\ k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum (Prob * (A ^\ k)) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Omega,Sigma,A) is Event of Sigma
(Omega,A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,A) is Event of Sigma
Prob . (Omega,Sigma,A) is V28() real ext-real Element of REAL
(Omega,Sigma,Prob,A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Omega,Sigma,Prob,A) is V28() real ext-real Element of REAL
Partial_Intersection (Omega,A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Partial_Intersection (Omega,A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Intersection (Omega,A))) . n is V28() real ext-real Element of REAL
dom (Prob * (Partial_Intersection (Omega,A))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Partial_Intersection (Omega,A)) . n is Event of Sigma
Prob . ((Partial_Intersection (Omega,A)) . n) is V28() real ext-real Element of REAL
Intersection (Partial_Intersection (Omega,A)) is Element of bool Omega
Complement (Partial_Intersection (Omega,A)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Partial_Intersection (Omega,A))) is Element of bool Omega
(Union (Complement (Partial_Intersection (Omega,A)))) ` is Element of bool Omega
Intersection (Omega,A) is Element of bool Omega
Complement (Omega,A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Omega,A)) is Element of bool Omega
(Union (Complement (Omega,A))) ` is Element of bool Omega
lim (Prob * (Partial_Intersection (Omega,A))) is V28() real ext-real Element of REAL
Prob . (Intersection (Partial_Intersection (Omega,A))) is V28() real ext-real set
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n ^\ k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Partial_Union (n ^\ k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Partial_Union (n ^\ k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Union (n ^\ k))) . n is V28() real ext-real Element of REAL
Prob * (n ^\ k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * (n ^\ k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Sums (Prob * (n ^\ k))) . n is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ k))) . 0 is V28() real ext-real Element of REAL
(Prob * (n ^\ k)) . 0 is V28() real ext-real Element of REAL
dom (Prob * (n ^\ k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(n ^\ k) . 0 is Event of Sigma
Prob . ((n ^\ k) . 0) is V28() real ext-real Element of REAL
(Partial_Union (n ^\ k)) . 0 is Event of Sigma
Prob . ((Partial_Union (n ^\ k)) . 0) is V28() real ext-real Element of REAL
dom (Prob * (Partial_Union (n ^\ k))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (Partial_Union (n ^\ k))) . 0 is V28() real ext-real set
(Partial_Sums (Prob * (n ^\ k))) . 0 is V28() real ext-real set
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Union (n ^\ k))) . B2 is V28() real ext-real set
(Partial_Sums (Prob * (n ^\ k))) . B2 is V28() real ext-real set
B2 + 1 is 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
(Prob * (Partial_Union (n ^\ k))) . (B2 + 1) is V28() real ext-real set
(Partial_Sums (Prob * (n ^\ k))) . (B2 + 1) is V28() real ext-real set
(Prob * (Partial_Union (n ^\ k))) . B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ k))) . B2 is V28() real ext-real Element of REAL
(Partial_Union (n ^\ k)) . B2 is Event of Sigma
(n ^\ k) . (B2 + 1) is Event of Sigma
((Partial_Union (n ^\ k)) . B2) \/ ((n ^\ k) . (B2 + 1)) is Event of Sigma
Prob . (((Partial_Union (n ^\ k)) . B2) \/ ((n ^\ k) . (B2 + 1))) is V28() real ext-real Element of REAL
Prob . ((Partial_Union (n ^\ k)) . B2) is V28() real ext-real Element of REAL
Prob . ((n ^\ k) . (B2 + 1)) is V28() real ext-real Element of REAL
(Prob . ((Partial_Union (n ^\ k)) . B2)) + (Prob . ((n ^\ k) . (B2 + 1))) is V28() real ext-real Element of REAL
(Prob * (n ^\ k)) . (B2 + 1) is V28() real ext-real Element of REAL
(Partial_Union (n ^\ k)) . (B2 + 1) is Event of Sigma
Prob . ((Partial_Union (n ^\ k)) . (B2 + 1)) is V28() real ext-real Element of REAL
(Prob . ((Partial_Union (n ^\ k)) . B2)) + ((Prob * (n ^\ k)) . (B2 + 1)) is V28() real ext-real Element of REAL
(Prob . ((Partial_Union (n ^\ k)) . (B2 + 1))) - (Prob . ((Partial_Union (n ^\ k)) . B2)) is V28() real ext-real Element of REAL
(Prob . ((Partial_Union (n ^\ k)) . (B2 + 1))) - ((Prob * (n ^\ k)) . (B2 + 1)) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * (n ^\ k))) . B2) + ((Prob * (n ^\ k)) . (B2 + 1)) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ k))) . (B2 + 1) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * A) ^\ n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * A)
Partial_Sums ((Prob * A) ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Prob * (n ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Prob * n) ^\ n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * n)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (n ^\ n)) . k is V28() real ext-real Element of REAL
((Prob * n) ^\ n) . k is V28() real ext-real Element of REAL
dom (Prob * (n ^\ n)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(n ^\ n) . k is Event of Sigma
Prob . ((n ^\ n) . k) is V28() real ext-real Element of REAL
dom (Prob * n) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . (n + k) is Event of Sigma
Prob . (n . (n + k)) is V28() real ext-real Element of REAL
(Prob * n) . (n + k) is V28() real ext-real Element of REAL
k + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * n) . (k + n) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Prob * (A ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * (A ^\ n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Prob * A) ^\ n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * A)
Partial_Sums ((Prob * A) ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Partial_Union (A ^\ n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Partial_Union (A ^\ n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Prob * (Partial_Union (A ^\ n))) is V28() real ext-real Element of REAL
Prob * (A ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * (A ^\ n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Partial_Sums (Prob * (A ^\ n))) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Union (A ^\ n))) . n is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (A ^\ n))) . n is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Union (A ^\ n) is Element of bool Omega
Prob . (Union (A ^\ n)) is V28() real ext-real set
Prob * (A ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * (A ^\ n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Partial_Sums (Prob * (A ^\ n))) is V28() real ext-real Element of REAL
Partial_Union (A ^\ n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Partial_Union (A ^\ n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Prob * (Partial_Union (A ^\ n))) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Union (A ^\ n) is Element of bool Omega
Prob . (Union (A ^\ n)) is V28() real ext-real set
Prob * (A ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum (Prob * (A ^\ n)) is V28() real ext-real Element of REAL
Partial_Sums (Prob * (A ^\ n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Partial_Sums (Prob * (A ^\ n))) is V28() real ext-real Element of REAL
Prob * (Omega,A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Omega,A)) . n is V28() real ext-real Element of REAL
(Omega,Sigma,Prob,A) . n is V28() real ext-real Element of REAL
dom (Prob * (Omega,A)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Omega,A) . n is Event of Sigma
Prob . ((Omega,A) . n) is V28() real ext-real Element of REAL
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Union (A ^\ n) is Element of bool Omega
Prob . (Union (A ^\ n)) is V28() real ext-real set
Prob * (A ^\ n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum (Prob * (A ^\ n)) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Intersection (Omega,A))) . n is V28() real ext-real Element of REAL
(Prob * (Omega,A)) . n is V28() real ext-real Element of REAL
(Partial_Intersection (Omega,A)) . n is Event of Sigma
Prob . ((Partial_Intersection (Omega,A)) . n) is V28() real ext-real Element of REAL
(Omega,A) . n is Event of Sigma
Prob . ((Omega,A) . n) is V28() real ext-real Element of REAL
dom (Prob * (Partial_Intersection (Omega,A))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom (Prob * (Omega,A)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Intersection (Omega,A))) . n is V28() real ext-real Element of REAL
(Omega,Sigma,Prob,A) . n is V28() real ext-real Element of REAL
(Prob * (Omega,A)) . n is V28() real ext-real Element of REAL
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Omega,Sigma,Prob,n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Omega,Sigma,Prob,n) is V28() real ext-real Element of REAL
Sum (Prob * n) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + 1 is 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
(Prob * n) ^\ (n + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * n)
Sum ((Prob * n) ^\ (n + 1)) is V28() real ext-real Element of REAL
(Sum (Prob * n)) - (Sum ((Prob * n) ^\ (n + 1))) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . n is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . n) + (Sum ((Prob * n) ^\ (n + 1))) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * n)) . n) + (Sum ((Prob * n) ^\ (n + 1)))) - (Sum ((Prob * n) ^\ (n + 1))) is V28() real ext-real Element of REAL
(Omega,Sigma,Prob,n) ^\ 1 is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,(Omega,Sigma,Prob,n))
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * n)) . n is V28() real ext-real Element of REAL
((Omega,Sigma,Prob,n) ^\ 1) . n is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * n)) . k is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . k) - ((Partial_Sums (Prob * n)) . n) is V28() real ext-real Element of REAL
abs (((Partial_Sums (Prob * n)) . k) - ((Partial_Sums (Prob * n)) . n)) is V28() real ext-real Element of REAL
((Omega,Sigma,Prob,n) ^\ 1) . k is V28() real ext-real Element of REAL
(((Omega,Sigma,Prob,n) ^\ 1) . k) - (((Omega,Sigma,Prob,n) ^\ 1) . n) is V28() real ext-real Element of REAL
abs ((((Omega,Sigma,Prob,n) ^\ 1) . k) - (((Omega,Sigma,Prob,n) ^\ 1) . n)) is V28() real ext-real Element of REAL
n + 1 is 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
(Prob * n) ^\ (n + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * n)
Sum ((Prob * n) ^\ (n + 1)) is V28() real ext-real Element of REAL
(Sum (Prob * n)) - (Sum ((Prob * n) ^\ (n + 1))) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . k) - ((Sum (Prob * n)) - (Sum ((Prob * n) ^\ (n + 1)))) is V28() real ext-real Element of REAL
k + 1 is 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
(Prob * n) ^\ (k + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * n)
Sum ((Prob * n) ^\ (k + 1)) is V28() real ext-real Element of REAL
(Sum (Prob * n)) - (Sum ((Prob * n) ^\ (k + 1))) is V28() real ext-real Element of REAL
((Sum (Prob * n)) - (Sum ((Prob * n) ^\ (k + 1)))) - ((Sum (Prob * n)) - (Sum ((Prob * n) ^\ (n + 1)))) is V28() real ext-real Element of REAL
(Sum ((Prob * n) ^\ (n + 1))) - (Sum ((Prob * n) ^\ (k + 1))) is V28() real ext-real Element of REAL
B2 is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * B2 is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 ^\ c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),B2)
Prob * (B2 ^\ c₉) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Prob * B2) ^\ c₉ is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * B2)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (B2 ^\ c₉)) . k is V28() real ext-real Element of REAL
((Prob * B2) ^\ c₉) . k is V28() real ext-real Element of REAL
dom (Prob * (B2 ^\ c₉)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(B2 ^\ c₉) . k is Event of Sigma
Prob . ((B2 ^\ c₉) . k) is V28() real ext-real Element of REAL
dom (Prob * B2) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
c₉ + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 . (c₉ + k) is Event of Sigma
Prob . (B2 . (c₉ + k)) is V28() real ext-real Element of REAL
(Prob * B2) . (c₉ + k) is V28() real ext-real Element of REAL
k + c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * B2) . (k + c₉) is V28() real ext-real Element of REAL
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Omega,Sigma,Prob,n) ^\ 1) . B2 is V28() real ext-real Element of REAL
B2 + 1 is 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
(Prob * n) ^\ (B2 + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * n)
Sum ((Prob * n) ^\ (B2 + 1)) is V28() real ext-real Element of REAL
(Omega,Sigma,Prob,n) . (B2 + 1) is V28() real ext-real Element of REAL
n ^\ (B2 + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Prob * (n ^\ (B2 + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum (Prob * (n ^\ (B2 + 1))) is V28() real ext-real Element of REAL
(((Omega,Sigma,Prob,n) ^\ 1) . n) - (((Omega,Sigma,Prob,n) ^\ 1) . k) is V28() real ext-real Element of REAL
abs ((((Omega,Sigma,Prob,n) ^\ 1) . n) - (((Omega,Sigma,Prob,n) ^\ 1) . k)) is V28() real ext-real Element of REAL
(((Omega,Sigma,Prob,n) ^\ 1) . n) - (Sum ((Prob * n) ^\ (k + 1))) is V28() real ext-real Element of REAL
- 0 is empty Relation-like non-empty empty-yielding RAT -valued functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V28() real V42() V44() ext-real non positive non negative V59() V60() V61() V62() V70() V71() V72() V73() V74() V75() V76() Element of REAL
- ((((Omega,Sigma,Prob,n) ^\ 1) . n) - (((Omega,Sigma,Prob,n) ^\ 1) . k)) is V28() real ext-real Element of REAL
- ((((Omega,Sigma,Prob,n) ^\ 1) . k) - (((Omega,Sigma,Prob,n) ^\ 1) . n)) is V28() real ext-real Element of REAL
- ((((Omega,Sigma,Prob,n) ^\ 1) . n) - (((Omega,Sigma,Prob,n) ^\ 1) . k)) is V28() real ext-real Element of REAL
n is V28() real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * n)) . k is V28() real ext-real Element of REAL
((Omega,Sigma,Prob,n) ^\ 1) . k is V28() real ext-real Element of REAL
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Omega,Sigma,Prob,n) ^\ 1) . B2 is V28() real ext-real Element of REAL
(((Omega,Sigma,Prob,n) ^\ 1) . B2) - (((Omega,Sigma,Prob,n) ^\ 1) . k) is V28() real ext-real Element of REAL
abs ((((Omega,Sigma,Prob,n) ^\ 1) . B2) - (((Omega,Sigma,Prob,n) ^\ 1) . k)) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . B2 is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . B2) - ((Partial_Sums (Prob * n)) . k) is V28() real ext-real Element of REAL
abs (((Partial_Sums (Prob * n)) . B2) - ((Partial_Sums (Prob * n)) . k)) is V28() real ext-real Element of REAL
n is V28() real ext-real set
((Omega,Sigma,Prob,n) ^\ 1) + (Partial_Sums (Prob * n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
dom (((Omega,Sigma,Prob,n) ^\ 1) + (Partial_Sums (Prob * n))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
NAT --> (Sum (Prob * n)) is non empty Relation-like NAT -defined REAL -valued Function-like constant V17( NAT ) V18( NAT , REAL ) T-Sequence-like V59() V60() V61() convergent Element of bool [:NAT,REAL:]
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (Sum (Prob * n))) . B2 is V28() real ext-real Element of REAL
n . B2 is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Omega,Sigma,Prob,n) ^\ 1) . c₉ is V28() real ext-real Element of REAL
c₉ + 1 is 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
(Prob * n) ^\ (c₉ + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * n)
Sum ((Prob * n) ^\ (c₉ + 1)) is V28() real ext-real Element of REAL
(Omega,Sigma,Prob,n) . (c₉ + 1) is V28() real ext-real Element of REAL
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * k is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k ^\ r is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),k)
Prob * (k ^\ r) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Prob * k) ^\ r is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * k)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (k ^\ r)) . n is V28() real ext-real Element of REAL
((Prob * k) ^\ r) . n is V28() real ext-real Element of REAL
dom (Prob * (k ^\ r)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(k ^\ r) . n is Event of Sigma
Prob . ((k ^\ r) . n) is V28() real ext-real Element of REAL
dom (Prob * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
r + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k . (r + n) is Event of Sigma
Prob . (k . (r + n)) is V28() real ext-real Element of REAL
(Prob * k) . (r + n) is V28() real ext-real Element of REAL
n + r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * k) . (n + r) is V28() real ext-real Element of REAL
n ^\ (c₉ + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Prob * (n ^\ (c₉ + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Sum (Prob * (n ^\ (c₉ + 1))) is V28() real ext-real Element of REAL
((Omega,Sigma,Prob,n) ^\ 1) . B2 is V28() real ext-real Element of REAL
B2 + 1 is 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
(Prob * n) ^\ (B2 + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() M16( REAL ,Prob * n)
Sum ((Prob * n) ^\ (B2 + 1)) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . B2 is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . B2) + (Sum ((Prob * n) ^\ (B2 + 1))) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . B2) + (((Omega,Sigma,Prob,n) ^\ 1) . B2) is V28() real ext-real Element of REAL
lim (NAT --> (Sum (Prob * n))) is V28() real ext-real Element of REAL
lim n is V28() real ext-real Element of REAL
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (Sum (Prob * n))) . B2 is V28() real ext-real Element of REAL
n . B2 is V28() real ext-real Element of REAL
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> (Sum (Prob * n))) . 1 is V28() real ext-real Element of REAL
lim ((Omega,Sigma,Prob,n) ^\ 1) is V28() real ext-real Element of REAL
lim (Partial_Sums (Prob * n)) is V28() real ext-real Element of REAL
(lim ((Omega,Sigma,Prob,n) ^\ 1)) + (lim (Partial_Sums (Prob * n))) is V28() real ext-real Element of REAL
(lim ((Omega,Sigma,Prob,n) ^\ 1)) + (Sum (Prob * n)) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is set
K496(Prob) is non empty Element of bool (bool Prob)
bool Prob is non empty set
bool (bool Prob) is non empty V94() set
[:NAT,K496(Prob):] is non empty Relation-like set
bool [:NAT,K496(Prob):] is non empty V94() set
A is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
n is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . k is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . k is Element of K496(Prob)
k + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (k + n) is Element of K496(Prob)
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (B2 + n) is Element of K496(Prob)
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . c₉ is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Element of K496(Prob)
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . c₉ is Element of K496(Prob)
Prob is set
K496(Prob) is non empty Element of bool (bool Prob)
bool Prob is non empty set
bool (bool Prob) is non empty V94() set
[:NAT,K496(Prob):] is non empty Relation-like set
bool [:NAT,K496(Prob):] is non empty V94() set
A is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
(Prob,A) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Intersection (Prob,A) is Element of bool Prob
Complement (Prob,A) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (Prob,A)) is Element of bool Prob
(Union (Complement (Prob,A))) ` is Element of bool Prob
n is set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob,A) . n is Element of K496(Prob)
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ n) is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . k is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob,A) . n is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob,A) . n is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Element of K496(Prob)
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Union (A ^\ n) is Element of bool Prob
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . B2 is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob,A) . n is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Element of K496(Prob)
Prob is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Prob) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,Prob) is Event of Sigma
A is set
Intersection (Omega,Prob) is Element of bool Omega
Complement (Omega,Prob) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Omega,Prob)) is Element of bool Omega
(Union (Complement (Omega,Prob))) ` is Element of bool Omega
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob is set
K496(Prob) is non empty Element of bool (bool Prob)
bool Prob is non empty set
bool (bool Prob) is non empty V94() set
[:NAT,K496(Prob):] is non empty Relation-like set
bool [:NAT,K496(Prob):] is non empty V94() set
A is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
(Prob,A) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Prob,A) is Element of bool Prob
n is set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob,A) . n is Element of K496(Prob)
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
Intersection (A ^\ n) is Element of bool Prob
Complement (A ^\ n) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ n)) is Element of bool Prob
(Union (Complement (A ^\ n))) ` is Element of bool Prob
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Element of K496(Prob)
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c<sub>9</sub> is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . c<sub>9</sub> is Element of K496(Prob)
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
the epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . B2 is Element of K496(Prob)
n + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (n + B2) is Element of K496(Prob)
Intersection (A ^\ n) is Element of bool Prob
Complement (A ^\ n) is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
Union (Complement (A ^\ n)) is Element of bool Prob
(Union (Complement (A ^\ n))) ` is Element of bool Prob
(Prob,A) . n is Element of K496(Prob)
Prob is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement Prob is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,(Complement Prob)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,(Complement Prob)) is Element of bool Omega
A is Element of Omega
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,(Complement Prob)) . n is Event of Sigma
(Complement Prob) ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega), Complement Prob)
Intersection ((Complement Prob) ^\ n) is Element of bool Omega
Complement ((Complement Prob) ^\ n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement ((Complement Prob) ^\ n)) is Element of bool Omega
(Union (Complement ((Complement Prob) ^\ n))) ` is Element of bool Omega
the epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Prob . k is Event of Sigma
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement Prob) . k is Event of Sigma
c<sub>9</sub> is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Complement Prob) ^\ n) . c<sub>9</sub> is Event of Sigma
(Prob . k) ` is Element of bool Omega
Omega \ (Prob . k) is Element of bool Omega
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement Prob) . k is Event of Sigma
Prob . k is Event of Sigma
Omega \ (Prob . k) is Element of bool Omega
(Prob . k) ` is Element of bool Omega
(Complement Prob) ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega), Complement Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Complement Prob) ^\ n) . k is Event of Sigma
n + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement Prob) . (n + k) is Event of Sigma
Intersection ((Complement Prob) ^\ n) is Element of bool Omega
Complement ((Complement Prob) ^\ n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement ((Complement Prob) ^\ n)) is Element of bool Omega
(Union (Complement ((Complement Prob) ^\ n))) ` is Element of bool Omega
(Omega,(Complement Prob)) . n is Event of Sigma
Prob is set
K496(Prob) is non empty Element of bool (bool Prob)
bool Prob is non empty set
bool (bool Prob) is non empty V94() set
[:NAT,K496(Prob):] is non empty Relation-like set
bool [:NAT,K496(Prob):] is non empty V94() set
B2 is set
K496(B2) is non empty Element of bool (bool B2)
bool B2 is non empty set
bool (bool B2) is non empty V94() set
[:NAT,K496(B2):] is non empty Relation-like set
bool [:NAT,K496(B2):] is non empty V94() set
m is set
K496(m) is non empty Element of bool (bool m)
bool m is non empty set
bool (bool m) is non empty V94() set
[:NAT,K496(m):] is non empty Relation-like set
bool [:NAT,K496(m):] is non empty V94() set
q is set
K496(q) is non empty Element of bool (bool q)
bool q is non empty set
bool (bool q) is non empty V94() set
[:NAT,K496(q):] is non empty Relation-like set
bool [:NAT,K496(q):] is non empty V94() set
k is set
K496(k) is non empty Element of bool (bool k)
bool k is non empty set
bool (bool k) is non empty V94() set
[:NAT,K496(k):] is non empty Relation-like set
bool [:NAT,K496(k):] is non empty V94() set
x is set
K496(x) is non empty Element of bool (bool x)
bool x is non empty set
bool (bool x) is non empty V94() set
[:NAT,K496(x):] is non empty Relation-like set
bool [:NAT,K496(x):] is non empty V94() set
n is set
A is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) Element of bool [:NAT,K496(Prob):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Prob) -valued Function-like V17( NAT ) V18( NAT ,K496(Prob)) M16(K496(Prob),A)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . k is Element of K496(Prob)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
r is set
c₉ is non empty Relation-like NAT -defined K496(B2) -valued Function-like V17( NAT ) V18( NAT ,K496(B2)) Element of bool [:NAT,K496(B2):]
c₉ . n is Element of K496(B2)
c₉ ^\ k is non empty Relation-like NAT -defined K496(B2) -valued Function-like V17( NAT ) V18( NAT ,K496(B2)) M16(K496(B2),c₉)
m is set
s is non empty Relation-like NAT -defined K496(m) -valued Function-like V17( NAT ) V18( NAT ,K496(m)) Element of bool [:NAT,K496(m):]
(m,s) is non empty Relation-like NAT -defined K496(m) -valued Function-like V17( NAT ) V18( NAT ,K496(m)) Element of bool [:NAT,K496(m):]
Intersection (m,s) is Element of bool m
Complement (m,s) is non empty Relation-like NAT -defined K496(m) -valued Function-like V17( NAT ) V18( NAT ,K496(m)) Element of bool [:NAT,K496(m):]
Union (Complement (m,s)) is Element of bool m
(Union (Complement (m,s))) ` is Element of bool m
z is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
knat is set
k is non empty Relation-like NAT -defined K496(q) -valued Function-like V17( NAT ) V18( NAT ,K496(q)) Element of bool [:NAT,K496(q):]
(q,k) is non empty Relation-like NAT -defined K496(q) -valued Function-like V17( NAT ) V18( NAT ,K496(q)) Element of bool [:NAT,K496(q):]
Intersection (q,k) is Element of bool q
Complement (q,k) is non empty Relation-like NAT -defined K496(q) -valued Function-like V17( NAT ) V18( NAT ,K496(q)) Element of bool [:NAT,K496(q):]
Union (Complement (q,k)) is Element of bool q
(Union (Complement (q,k))) ` is Element of bool q
B is set
j is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,j) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,j) is Event of Sigma
A is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
C is set
B is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,B) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,B) is Event of Sigma
e is set
n is non empty Relation-like NAT -defined K496(k) -valued Function-like V17( NAT ) V18( NAT ,K496(k)) Element of bool [:NAT,K496(k):]
(k,n) is non empty Relation-like NAT -defined K496(k) -valued Function-like V17( NAT ) V18( NAT ,K496(k)) Element of bool [:NAT,K496(k):]
Union (k,n) is Element of bool k
c₃₁ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
knat is set
knat is non empty Relation-like NAT -defined K496(x) -valued Function-like V17( NAT ) V18( NAT ,K496(x)) Element of bool [:NAT,K496(x):]
(x,knat) is non empty Relation-like NAT -defined K496(x) -valued Function-like V17( NAT ) V18( NAT ,K496(x)) Element of bool [:NAT,K496(x):]
Union (x,knat) is Element of bool x
c₃₃ is set
c₃₂ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,c₃₂) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,c₃₂) is Element of bool Omega
c₃₆ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₃₅ is set
c₃₄ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,c₃₄) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,c₃₄) is Element of bool Omega
c₃₈ is Element of Omega
c₃₇ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement c₃₇ is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,(Complement c₃₇)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,(Complement c₃₇)) is Element of bool Omega
c₄₁ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₄₀ is Element of Omega
c₃₉ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement c₃₉ is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,(Complement c₃₉)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,(Complement c₃₉)) is Element of bool Omega
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
lim_sup A is Element of bool Omega
superior_setsequence A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
Intersection (superior_setsequence A) is Element of bool Omega
Complement (superior_setsequence A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (superior_setsequence A)) is Element of bool Omega
(Union (Complement (superior_setsequence A))) ` is Element of bool Omega
(Omega,Sigma,A) is Event of Sigma
(Omega,A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,A) is Event of Sigma
lim_inf A is Element of bool Omega
inferior_setsequence A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
K528(Omega,(inferior_setsequence A)) is Element of bool Omega
(Omega,Sigma,A) is Event of Sigma
(Omega,A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,A) is Element of bool Omega
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Sigma,(Complement A)) is Event of Sigma
(Omega,Sigma,A) ` is Element of bool Omega
Prob . (Omega,Sigma,(Complement A)) is V28() real ext-real Element of REAL
Prob . (Omega,Sigma,A) is V28() real ext-real Element of REAL
(Prob . (Omega,Sigma,(Complement A))) + (Prob . (Omega,Sigma,A)) is V28() real ext-real Element of REAL
lim_inf (Complement A) is Element of bool Omega
inferior_setsequence (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
K528(Omega,(inferior_setsequence (Complement A))) is Element of bool Omega
Prob . (lim_inf (Complement A)) is V28() real ext-real set
Prob . (lim_sup A) is V28() real ext-real set
(Prob . (lim_inf (Complement A))) + (Prob . (lim_sup A)) is V28() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
n is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . k is Event of Sigma
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . k is Event of Sigma
k + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (k + n) is Event of Sigma
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (B2 + n) is Event of Sigma
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . c₉ is Event of Sigma
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Event of Sigma
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Event of Sigma
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
n + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . c₉ is Event of Sigma
n is set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . k is Event of Sigma
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(A ^\ n) . k is Event of Sigma
n + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (n + k) is Event of Sigma
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
A . (n + k) is Event of Sigma
A ^\ n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
(A ^\ n) . k is Event of Sigma
n is set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
lim_inf n is Element of bool Omega
inferior_setsequence n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
K528(Omega,(inferior_setsequence n)) is Element of bool Omega
(Omega,Sigma,n) is Event of Sigma
(Omega,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,n) is Element of bool Omega
n is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . (k + B2) is Event of Sigma
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . B2 is Event of Sigma
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
k + c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . (k + k) is Event of Sigma
n is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n is set
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Sigma,n) is Event of Sigma
(Omega,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,n) is Element of bool Omega
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega \ (Omega,Sigma,A) is Element of bool Omega
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
[#] Sigma is Event of Sigma
([#] Sigma) \ (Omega,Sigma,A) is Event of Sigma
Prob . (([#] Sigma) \ (Omega,Sigma,A)) is V28() real ext-real Element of REAL
(Prob . (([#] Sigma) \ (Omega,Sigma,A))) + (Prob . (Omega,Sigma,A)) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim_sup A is Element of bool Omega
superior_setsequence A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
Intersection (superior_setsequence A) is Element of bool Omega
Complement (superior_setsequence A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (superior_setsequence A)) is Element of bool Omega
(Union (Complement (superior_setsequence A))) ` is Element of bool Omega
Prob . (lim_sup A) is V28() real ext-real set
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
lim_inf (Complement A) is Element of bool Omega
inferior_setsequence (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
K528(Omega,(inferior_setsequence (Complement A))) is Element of bool Omega
Prob . (lim_inf (Complement A)) is V28() real ext-real set
(Omega,Sigma,(Complement A)) is Event of Sigma
Prob . (Omega,Sigma,(Complement A)) is V28() real ext-real Element of REAL
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Complement n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Sigma,(Complement n)) is Event of Sigma
Prob . (Omega,Sigma,(Complement n)) is V28() real ext-real Element of REAL
(Omega,Sigma,Prob,n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Omega,Sigma,Prob,n) is V28() real ext-real Element of REAL
(Omega,Sigma,n) is Event of Sigma
(Omega,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,n) is Event of Sigma
Prob . (Omega,Sigma,n) is V28() real ext-real Element of REAL
(Prob . (Omega,Sigma,n)) + (Prob . (Omega,Sigma,(Complement n))) is V28() real ext-real Element of REAL
0 + (Prob . (Omega,Sigma,(Complement n))) is V28() real ext-real Element of REAL
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim_sup n is Element of bool Omega
superior_setsequence n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
Intersection (superior_setsequence n) is Element of bool Omega
Complement (superior_setsequence n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (superior_setsequence n)) is Element of bool Omega
(Union (Complement (superior_setsequence n))) ` is Element of bool Omega
Prob . (lim_sup n) is V28() real ext-real set
(Omega,Sigma,n) is Event of Sigma
(Omega,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,n) is Event of Sigma
Prob . (Omega,Sigma,n) is V28() real ext-real Element of REAL
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Complement n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
lim_inf (Complement n) is Element of bool Omega
inferior_setsequence (Complement n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
K528(Omega,(inferior_setsequence (Complement n))) is Element of bool Omega
Prob . (lim_inf (Complement n)) is V28() real ext-real set
lim_sup n is Element of bool Omega
superior_setsequence n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
Intersection (superior_setsequence n) is Element of bool Omega
Complement (superior_setsequence n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (superior_setsequence n)) is Element of bool Omega
(Union (Complement (superior_setsequence n))) ` is Element of bool Omega
Prob . (lim_sup n) is V28() real ext-real set
(Omega,Sigma,n) is Event of Sigma
(Omega,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,n) is Event of Sigma
Prob . (Omega,Sigma,n) is V28() real ext-real Element of REAL
(Omega,Sigma,(Complement n)) is Event of Sigma
Prob . (Omega,Sigma,(Complement n)) is V28() real ext-real Element of REAL
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Complement n is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Sigma,(Complement n)) is Event of Sigma
Prob . (Omega,Sigma,(Complement n)) is V28() real ext-real Element of REAL
(Omega,Sigma,n) is Event of Sigma
(Omega,n) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
@Intersection (Omega,n) is Event of Sigma
Prob . (Omega,Sigma,n) is V28() real ext-real Element of REAL
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
inferior_setsequence k is non empty Relation-like NAT -defined Sigma -valued K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
(Omega,(Complement n)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,Sigma,k) is Event of Sigma
(Omega,k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Omega,k) is Element of bool Omega
Prob . (Omega,Sigma,k) is V28() real ext-real Element of REAL
Prob * (Omega,(Complement n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Prob * (Omega,(Complement n))) is V28() real ext-real Element of REAL
B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Omega,(Complement n))) . B2 is V28() real ext-real Element of REAL
dom (Prob * (Omega,(Complement n))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Omega,(Complement n)) . B2 is Event of Sigma
Prob . ((Omega,(Complement n)) . B2) is V28() real ext-real Element of REAL
(Complement n) ^\ B2 is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega), Complement n)
Intersection ((Complement n) ^\ B2) is Element of bool Omega
Complement ((Complement n) ^\ B2) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement ((Complement n) ^\ B2)) is Element of bool Omega
(Union (Complement ((Complement n) ^\ B2))) ` is Element of bool Omega
Partial_Intersection ((Complement n) ^\ B2) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Intersection (Partial_Intersection ((Complement n) ^\ B2)) is Element of bool Omega
Complement (Partial_Intersection ((Complement n) ^\ B2)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (Partial_Intersection ((Complement n) ^\ B2))) is Element of bool Omega
(Union (Complement (Partial_Intersection ((Complement n) ^\ B2)))) ` is Element of bool Omega
Prob . (Intersection (Partial_Intersection ((Complement n) ^\ B2))) is V28() real ext-real set
Prob * (Partial_Intersection ((Complement n) ^\ B2)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim (Prob * (Partial_Intersection ((Complement n) ^\ B2))) is V28() real ext-real Element of REAL
n ^\ B2 is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
Complement (n ^\ B2) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement (n ^\ B2)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Partial_Intersection (Complement (n ^\ B2))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob * (n ^\ B2) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * (n ^\ B2)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
1 + (Partial_Sums (Prob * (n ^\ B2))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(1 + (Partial_Sums (Prob * (n ^\ B2)))) " is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Intersection (Complement (n ^\ B2)))) . c₉ is V28() real ext-real Element of REAL
((1 + (Partial_Sums (Prob * (n ^\ B2)))) ") . c₉ is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n ^\ k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),n)
r is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * r is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * r) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Intersection r is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is non empty Relation-like NAT -defined NAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(k) is non empty Relation-like NAT -defined NAT -valued Function-like one-to-one V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n * (k) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
m is set
(n ^\ k) . m is set
(n * (k)) . m is set
dom (n * (k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n * (k)) . s is Event of Sigma
(k) . s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . ((k) . s) is Event of Sigma
s + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k) * n is non empty Relation-like NAT -defined NAT -valued RAT -valued Function-like V17( NAT ) V18( NAT , NAT ) V59() V60() V61() V62() Element of bool [:NAT,NAT:]
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n * (k)) . (n . m) is Event of Sigma
((k) * n) . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . (((k) * n) . m) is Event of Sigma
dom (n * (k)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom ((k) * n) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(k) . (n . m) is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . ((k) . (n . m)) is Event of Sigma
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((k) * n) . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . (((k) * n) . m) is Event of Sigma
r . m is Event of Sigma
n . m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n * (k)) . (n . m) is Event of Sigma
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * r)) . m is V28() real ext-real Element of REAL
(Partial_Intersection r) . m is Event of Sigma
Prob . ((Partial_Intersection r) . m) is V28() real ext-real Element of REAL
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement k is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Complement k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob * k is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
1 + (Partial_Sums (Prob * k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
r is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Product (Prob * (Complement k))) . r is V28() real ext-real Element of REAL
(1 + (Partial_Sums (Prob * k))) . r is V28() real ext-real Element of REAL
((1 + (Partial_Sums (Prob * k))) . r) " is V28() real ext-real Element of REAL
(Partial_Sums (Prob * k)) . r is V28() real ext-real Element of REAL
1 + ((Partial_Sums (Prob * k)) . r) is V28() real ext-real Element of REAL
1 / (1 + ((Partial_Sums (Prob * k)) . r)) is V28() real ext-real Element of COMPLEX
((Prob * k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product ((Prob * k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product ((Prob * k))) . r is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * k)) . r) is V28() real ext-real Element of REAL
exp_R . (- ((Partial_Sums (Prob * k)) . r)) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * k) . n is V28() real ext-real Element of REAL
dom (Prob * k) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
k . n is Event of Sigma
Prob . (k . n) is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * k)) . n is V28() real ext-real Element of REAL
(Partial_Sums (Prob * k)) . 0 is V28() real ext-real Element of REAL
(Prob * k) . 0 is V28() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * k)) . m is V28() real ext-real Element of REAL
m + 1 is 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
(Partial_Sums (Prob * k)) . (m + 1) is V28() real ext-real Element of REAL
(Prob * k) . (m + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * k)) . m) + ((Prob * k) . (m + 1)) is V28() real ext-real Element of REAL
n is V28() real ext-real Element of REAL
- n is V28() real ext-real Element of REAL
exp_R . (- n) is V28() real ext-real Element of REAL
1 + n is V28() real ext-real Element of REAL
1 / (1 + n) is V28() real ext-real Element of COMPLEX
exp_R n is V28() real ext-real Element of REAL
exp_R . n is V28() real ext-real Element of REAL
exp_R (- n) is V28() real ext-real Element of REAL
exp_R . (- n) is V28() real ext-real Element of REAL
(exp_R n) * (exp_R (- n)) is V28() real ext-real Element of REAL
n + (- n) is V28() real ext-real Element of REAL
exp_R (n + (- n)) is V28() real ext-real Element of REAL
exp_R . (n + (- n)) is V28() real ext-real Element of REAL
(exp_R . (- n)) * (1 + n) is V28() real ext-real Element of REAL
n is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * n is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * n) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
1 + (Partial_Sums (Prob * n)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * n)) . m is V28() real ext-real Element of REAL
1 + ((Partial_Sums (Prob * n)) . m) is V28() real ext-real Element of REAL
1 / (1 + ((Partial_Sums (Prob * n)) . m)) is V28() real ext-real Element of COMPLEX
(1 + (Partial_Sums (Prob * n))) . m is V28() real ext-real Element of REAL
((1 + (Partial_Sums (Prob * n))) . m) " is V28() real ext-real Element of REAL
1 / ((1 + (Partial_Sums (Prob * n))) . m) is V28() real ext-real Element of COMPLEX
1 * (((1 + (Partial_Sums (Prob * n))) . m) ") is V28() real ext-real Element of REAL
dom (Prob * (Partial_Intersection (Complement (n ^\ B2)))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Partial_Intersection (Complement (n ^\ B2))) . c₉ is Event of Sigma
Prob . ((Partial_Intersection (Complement (n ^\ B2))) . c₉) is V28() real ext-real Element of REAL
Prob * (Complement (n ^\ B2)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement (n ^\ B2))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (Complement (n ^\ B2)))) . c₉ is V28() real ext-real Element of REAL
(1 + (Partial_Sums (Prob * (n ^\ B2)))) . c₉ is V28() real ext-real Element of REAL
((1 + (Partial_Sums (Prob * (n ^\ B2)))) . c₉) " is V28() real ext-real Element of REAL
B2 - 1 is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * n)) . c₉ is V28() real ext-real Element of REAL
- ((Partial_Sums (Prob * n)) . c₉) is V28() real ext-real Element of REAL
NAT --> (- ((Partial_Sums (Prob * n)) . c₉)) is non empty Relation-like NAT -defined REAL -valued Function-like constant V17( NAT ) V18( NAT , REAL ) T-Sequence-like V59() V60() V61() convergent Element of bool [:NAT,REAL:]
(Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
r is V28() real ext-real Element of REAL
n is V28() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . m is V28() real ext-real Element of REAL
m - B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ B2))) . (m - B2) is V28() real ext-real set
s is epsilon-transitive epsilon-connected ordinal natural V28() real ext-real non negative set
B2 + s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + 0 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . (B2 + 0) is V28() real ext-real Element of REAL
(B2 + 0) - B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ B2))) . ((B2 + 0) - B2) is V28() real ext-real set
dom ((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . B2 is V28() real ext-real Element of REAL
(NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . B2 is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . B2) + ((NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . B2) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . (B2 - 1) is V28() real ext-real set
- ((Partial_Sums (Prob * n)) . (B2 - 1)) is V28() real ext-real set
((Partial_Sums (Prob * n)) . B2) + (- ((Partial_Sums (Prob * n)) . (B2 - 1))) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . B2) - ((Partial_Sums (Prob * n)) . (B2 - 1)) is V28() real ext-real Element of REAL
(B2 - 1) + 1 is V28() real ext-real Element of REAL
(Prob * n) . ((B2 - 1) + 1) is V28() real ext-real set
((Partial_Sums (Prob * n)) . (B2 - 1)) + ((Prob * n) . ((B2 - 1) + 1)) is V28() real ext-real set
(((Partial_Sums (Prob * n)) . (B2 - 1)) + ((Prob * n) . ((B2 - 1) + 1))) - ((Partial_Sums (Prob * n)) . (B2 - 1)) is V28() real ext-real set
dom (Prob * (n ^\ B2)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Prob * (n ^\ B2)) . 0 is V28() real ext-real Element of REAL
(n ^\ B2) . 0 is Event of Sigma
Prob . ((n ^\ B2) . 0) is V28() real ext-real Element of REAL
0 + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n . (0 + B2) is Event of Sigma
dom (Prob * n) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
z is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + z is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . (B2 + z) is V28() real ext-real Element of REAL
(B2 + z) - B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ B2))) . ((B2 + z) - B2) is V28() real ext-real set
z + 1 is 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
B2 + (z + 1) is 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
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . (B2 + (z + 1)) is V28() real ext-real Element of REAL
(B2 + (z + 1)) - B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ B2))) . ((B2 + (z + 1)) - B2) is V28() real ext-real set
dom ((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(B2 + z) + 1 is 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
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . ((B2 + z) + 1) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . ((B2 + z) + 1) is V28() real ext-real Element of REAL
(NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . ((B2 + z) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . ((B2 + z) + 1)) + ((NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . ((B2 + z) + 1)) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . (B2 + z) is V28() real ext-real Element of REAL
(Prob * n) . ((B2 + z) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . (B2 + z)) + ((Prob * n) . ((B2 + z) + 1)) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * n)) . (B2 + z)) + ((Prob * n) . ((B2 + z) + 1))) + ((NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . ((B2 + z) + 1)) is V28() real ext-real Element of REAL
(Partial_Sums (Prob * n)) . (B2 - 1) is V28() real ext-real set
- ((Partial_Sums (Prob * n)) . (B2 - 1)) is V28() real ext-real set
(((Partial_Sums (Prob * n)) . (B2 + z)) + ((Prob * n) . ((B2 + z) + 1))) + (- ((Partial_Sums (Prob * n)) . (B2 - 1))) is V28() real ext-real Element of REAL
(NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . (B2 + z) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * n)) . (B2 + z)) + ((Prob * n) . ((B2 + z) + 1))) + ((NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . (B2 + z)) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * n)) . (B2 + z)) + ((NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . (B2 + z)) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * n)) . (B2 + z)) + ((NAT --> (- ((Partial_Sums (Prob * n)) . c₉))) . (B2 + z))) + ((Prob * n) . ((B2 + z) + 1)) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * (n ^\ B2))) . ((B2 + z) - B2)) + ((Prob * n) . ((B2 + z) + 1)) is V28() real ext-real Element of REAL
((B2 + z) - B2) + 1 is V28() real ext-real Element of REAL
(Prob * (n ^\ B2)) . (((B2 + z) - B2) + 1) is V28() real ext-real set
dom (Prob * (n ^\ B2)) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(n ^\ B2) . (z + 1) is Event of Sigma
Prob . ((n ^\ B2) . (z + 1)) is V28() real ext-real Element of REAL
n . (B2 + (z + 1)) is Event of Sigma
dom (Prob * n) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
B2 + m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . (B2 + m) is V28() real ext-real Element of REAL
(B2 + m) - B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ B2))) . ((B2 + m) - B2) is V28() real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
s + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . (s + B2) is V28() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * (n ^\ B2))) . m is V28() real ext-real Element of REAL
m + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
((Partial_Sums (Prob * n)) + (NAT --> (- ((Partial_Sums (Prob * n)) . c₉)))) . (m + B2) is V28() real ext-real Element of REAL
(m + B2) - B2 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (n ^\ B2))) . ((m + B2) - B2) is V28() real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
c₉ is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * c₉ is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * c₉) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
1 + (Partial_Sums (Prob * c₉)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(1 + (Partial_Sums (Prob * c₉))) " is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
lim ((1 + (Partial_Sums (Prob * c₉))) ") is V28() real ext-real Element of REAL
k is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * k is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * k) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
1 + (Partial_Sums (Prob * k)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
r is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(1 + (Partial_Sums (Prob * k))) . m is V28() real ext-real Element of REAL
(Partial_Sums (Prob * k)) . m is V28() real ext-real Element of REAL
((Partial_Sums (Prob * k)) . m) + 1 is V28() real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(1 + (Partial_Sums (Prob * k))) . m is V28() real ext-real Element of REAL
k is V28() real ext-real Element of REAL
k is V28() real ext-real Element of REAL
lim ((1 + (Partial_Sums (Prob * (n ^\ B2)))) ") is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * (Partial_Intersection (Complement (n ^\ B2)))) . c₉ is V28() real ext-real Element of REAL
dom (Prob * (Partial_Intersection (Complement (n ^\ B2)))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Partial_Intersection (Complement (n ^\ B2))) . c₉ is Event of Sigma
Prob . ((Partial_Intersection (Complement (n ^\ B2))) . c₉) is V28() real ext-real Element of REAL
lim (Prob * (Partial_Intersection (Complement (n ^\ B2)))) is V28() real ext-real Element of REAL
c₉ is set
(Complement (n ^\ B2)) . c₉ is set
((Complement n) ^\ B2) . c₉ is set
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement (n ^\ B2)) . k is Event of Sigma
(n ^\ B2) . k is Event of Sigma
((n ^\ B2) . k) ` is Element of bool Omega
((Complement n) ^\ B2) . k is Event of Sigma
k + B2 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Complement n) . (k + B2) is Event of Sigma
n . (k + B2) is Event of Sigma
(n . (k + B2)) ` is Element of bool Omega
NAT --> 0 is non empty Relation-like NAT -defined REAL -valued NAT -valued RAT -valued INT -valued Function-like constant V17( NAT ) V18( NAT , REAL ) T-Sequence-like V59() V60() V61() V62() convergent Element of bool [:NAT,REAL:]
(NAT --> 0) . 1 is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative Element of REAL
lim (NAT --> 0) is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> 0) . c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> 0) . c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative Element of REAL
(Prob * (Omega,(Complement n))) . c₉ is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(NAT --> 0) . c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative Element of REAL
(Prob * (Omega,(Complement n))) . c₉ is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob . (Omega,Sigma,(Complement n))) + (Prob . (Omega,Sigma,n)) is V28() real ext-real Element of REAL
c₉ is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
lim_inf (Complement A) is Element of bool Omega
inferior_setsequence (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
K528(Omega,(inferior_setsequence (Complement A))) is Element of bool Omega
Prob . (lim_inf (Complement A)) is V28() real ext-real set
lim_sup A is Element of bool Omega
superior_setsequence A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
Intersection (superior_setsequence A) is Element of bool Omega
Complement (superior_setsequence A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (superior_setsequence A)) is Element of bool Omega
(Union (Complement (superior_setsequence A))) ` is Element of bool Omega
Prob . (lim_sup A) is V28() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Prob * A) . n is V28() real ext-real Element of REAL
dom (Prob * A) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
A . n is Event of Sigma
Prob . (A . n) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
lim_inf (Complement A) is Element of bool Omega
inferior_setsequence (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-descending Element of bool [:NAT,K496(Omega):]
K528(Omega,(inferior_setsequence (Complement A))) is Element of bool Omega
Prob . (lim_inf (Complement A)) is V28() real ext-real set
lim_sup A is Element of bool Omega
superior_setsequence A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) non-ascending Element of bool [:NAT,K496(Omega):]
Intersection (superior_setsequence A) is Element of bool Omega
Complement (superior_setsequence A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Union (Complement (superior_setsequence A)) is Element of bool Omega
(Union (Complement (superior_setsequence A))) ` is Element of bool Omega
Prob . (lim_sup A) is V28() real ext-real set
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
n + 1 is 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
A ^\ (n + 1) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) M16(K496(Omega),A)
Prob * (A ^\ (n + 1)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Sums (Prob * (A ^\ (n + 1))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Sums (Prob * A)) . n is V28() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * (A ^\ (n + 1)))) . n is V28() real ext-real Element of REAL
(n + 1) + n is 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
(Partial_Sums (Prob * A)) . ((n + 1) + n) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . ((n + 1) + n)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
dom (Prob * (A ^\ (n + 1))) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
dom (Prob * A) is non empty V70() V71() V72() V73() V74() V75() Element of bool NAT
(Partial_Sums (Prob * A)) . (n + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . (n + 1)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
(Prob * A) . (n + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . n) + ((Prob * A) . (n + 1)) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * A)) . n) + ((Prob * A) . (n + 1))) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
(A ^\ (n + 1)) . 0 is Event of Sigma
Prob . ((A ^\ (n + 1)) . 0) is V28() real ext-real Element of REAL
(n + 1) + 0 is 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
A . ((n + 1) + 0) is Event of Sigma
Prob . (A . ((n + 1) + 0)) is V28() real ext-real Element of REAL
A . (n + 1) is Event of Sigma
Prob . (A . (n + 1)) is V28() real ext-real Element of REAL
(Prob * (A ^\ (n + 1))) . 0 is V28() real ext-real Element of REAL
(Partial_Sums (Prob * (A ^\ (n + 1)))) . 0 is V28() real ext-real Element of REAL
0 + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(0 + n) + 1 is 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
(Partial_Sums (Prob * A)) . ((0 + n) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . ((0 + n) + 1)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Sums (Prob * (A ^\ (n + 1)))) . k is V28() real ext-real Element of REAL
k + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(k + n) + 1 is 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
(Partial_Sums (Prob * A)) . ((k + n) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . ((k + n) + 1)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
k + 1 is 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
(Partial_Sums (Prob * (A ^\ (n + 1)))) . (k + 1) is V28() real ext-real Element of REAL
(k + 1) + n is 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
((k + 1) + n) + 1 is 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
(Partial_Sums (Prob * A)) . (((k + 1) + n) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . (((k + 1) + n) + 1)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
(Prob * (A ^\ (n + 1))) . (k + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * (A ^\ (n + 1)))) . k) + ((Prob * (A ^\ (n + 1))) . (k + 1)) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * A)) . ((k + n) + 1)) - ((Partial_Sums (Prob * A)) . n)) + ((Prob * (A ^\ (n + 1))) . (k + 1)) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * (A ^\ (n + 1)))) . (k + 1)) + ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . ((k + n) + 1)) + ((Prob * (A ^\ (n + 1))) . (k + 1)) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * A)) . ((k + n) + 1)) + ((Prob * (A ^\ (n + 1))) . (k + 1))) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
((((Partial_Sums (Prob * A)) . ((k + n) + 1)) + ((Prob * (A ^\ (n + 1))) . (k + 1))) - ((Partial_Sums (Prob * A)) . n)) + ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * (A ^\ (n + 1)))) . (k + 1)) + ((Partial_Sums (Prob * A)) . n)) - ((Partial_Sums (Prob * A)) . ((k + n) + 1)) is V28() real ext-real Element of REAL
((Prob * (A ^\ (n + 1))) . (k + 1)) + ((Partial_Sums (Prob * A)) . ((k + n) + 1)) is V28() real ext-real Element of REAL
(((Prob * (A ^\ (n + 1))) . (k + 1)) + ((Partial_Sums (Prob * A)) . ((k + n) + 1))) - ((Partial_Sums (Prob * A)) . ((k + n) + 1)) is V28() real ext-real Element of REAL
(A ^\ (n + 1)) . (k + 1) is Event of Sigma
(n + 1) + (k + 1) is 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
A . ((n + 1) + (k + 1)) is Event of Sigma
Prob . ((A ^\ (n + 1)) . (k + 1)) is V28() real ext-real Element of REAL
n + k is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n + k) + 2 is 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
(Prob * A) . ((n + k) + 2) is V28() real ext-real Element of REAL
((((Partial_Sums (Prob * (A ^\ (n + 1)))) . (k + 1)) + ((Partial_Sums (Prob * A)) . n)) - ((Partial_Sums (Prob * A)) . ((k + n) + 1))) + ((Partial_Sums (Prob * A)) . ((k + n) + 1)) is V28() real ext-real Element of REAL
((Prob * A) . ((n + k) + 2)) + ((Partial_Sums (Prob * A)) . ((k + n) + 1)) is V28() real ext-real Element of REAL
((k + n) + 1) + 1 is 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
(Partial_Sums (Prob * A)) . (((k + n) + 1) + 1) is V28() real ext-real Element of REAL
(Prob * A) . (((k + n) + 1) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . ((k + n) + 1)) + ((Prob * A) . (((k + n) + 1) + 1)) is V28() real ext-real Element of REAL
(((Partial_Sums (Prob * (A ^\ (n + 1)))) . (k + 1)) + ((Partial_Sums (Prob * A)) . n)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
(k + n) + 2 is 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
(Partial_Sums (Prob * A)) . ((k + n) + 2) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . ((k + n) + 2)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
n + n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(n + n) + 1 is 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
(Partial_Sums (Prob * A)) . ((n + n) + 1) is V28() real ext-real Element of REAL
((Partial_Sums (Prob * A)) . ((n + n) + 1)) - ((Partial_Sums (Prob * A)) . n) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,(Complement A)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Omega,A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Omega,(Complement A)) . n is Event of Sigma
Prob . ((Omega,(Complement A)) . n) is V28() real ext-real Element of REAL
(Omega,A) . n is Event of Sigma
Prob . ((Omega,A) . n) is V28() real ext-real Element of REAL
1 - (Prob . ((Omega,A) . n)) is V28() real ext-real Element of REAL
((Omega,A) . n) ` is Element of bool Omega
Prob . (((Omega,A) . n) `) is V28() real ext-real set
[#] Sigma is Event of Sigma
([#] Sigma) \ ((Omega,A) . n) is Event of Sigma
Prob . (([#] Sigma) \ ((Omega,A) . n)) is V28() real ext-real Element of REAL
Omega is non empty set
bool Omega is non empty V94() set
bool (bool Omega) is non empty V94() set
K496(Omega) is non empty V94() Element of bool (bool Omega)
[:NAT,K496(Omega):] is non empty Relation-like set
bool [:NAT,K496(Omega):] is non empty V94() set
Sigma is non empty compl-closed sigma-multiplicative Element of bool (bool Omega)
Prob is non empty Relation-like Sigma -defined REAL -valued Function-like V17(Sigma) V18(Sigma, REAL ) V59() V60() V61() Probability of Sigma
A is non empty Relation-like NAT -defined K496(Omega) -valued Sigma -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Complement A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * A is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Union A is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Prob * (Complement A) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V28() real V30() V31() ext-real non negative V70() V71() V72() V73() V74() V75() Element of NAT
(Partial_Intersection A) . n is Event of Sigma
Prob . ((Partial_Intersection A) . n) is V28() real ext-real Element of REAL
(Partial_Product (Prob * A)) . n is V28() real ext-real Element of REAL
(Partial_Union A) . n is Event of Sigma
Prob . ((Partial_Union A) . n) is V28() real ext-real Element of REAL
1 - (Prob . ((Partial_Union A) . n)) is V28() real ext-real Element of REAL
(Partial_Product (Prob * (Complement A))) . n is V28() real ext-real Element of REAL
Complement (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
Partial_Intersection (Complement (Complement A)) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (Complement (Complement A))) . n is Event of Sigma
Prob * (Complement (Complement A)) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
Partial_Product (Prob * (Complement (Complement A))) is non empty Relation-like NAT -defined REAL -valued Function-like V17( NAT ) V18( NAT , REAL ) V59() V60() V61() Element of bool [:NAT,REAL:]
(Partial_Product (Prob * (Complement (Complement A)))) . n is V28() real ext-real Element of REAL
Prob . ((Partial_Intersection (Complement (Complement A))) . n) is V28() real ext-real Element of REAL
Partial_Intersection (Complement A) is non empty Relation-like NAT -defined K496(Omega) -valued Function-like V17( NAT ) V18( NAT ,K496(Omega)) Element of bool [:NAT,K496(Omega):]
(Partial_Intersection (Complement A)) . n is Event of Sigma
Prob . ((Partial_Intersection (Complement A)) . n) is V28() real ext-real Element of REAL