theorem Th5: :: BOR_CANT:5

for Omega being non empty set
for Sigma being SigmaField of Omega
for Prob being Probability of Sigma
for n, n1, n2 being Nat holds
( ( for A, B being SetSequence of Sigma st n > n1 & B = A * (Special_Function (n1,n2)) holds
(Partial_Product (Prob * B)) . n = ((Partial_Product (Prob * A)) . n1) * ((Partial_Product (Prob * (A ^\ ((n1 + n2) + 1)))) . ((n - n1) - 1)) ) & ( for A, B, C being SetSequence of Sigma
for e being sequence of NAT st n > n1 & C = A * e & B = C * (Special_Function (n1,n2)) holds
(Partial_Intersection B) . n = ((Partial_Intersection C) . n1) /\ ((Partial_Intersection (C ^\ ((n1 + n2) + 1))) . ((n - n1) - 1)) ) )