let n be Nat; :: thesis: for Omega being non empty set
for Sigma being SigmaField of Omega
for ASeq being SetSequence of Sigma
for P being Probability of Sigma holds (P * ASeq) . n >= 0
let Omega be non empty set ; :: thesis: for Sigma being SigmaField of Omega
for ASeq being SetSequence of Sigma
for P being Probability of Sigma holds (P * ASeq) . n >= 0
let Sigma be SigmaField of Omega; :: thesis: for ASeq being SetSequence of Sigma
for P being Probability of Sigma holds (P * ASeq) . n >= 0
let ASeq be SetSequence of Sigma; :: thesis: for P being Probability of Sigma holds (P * ASeq) . n >= 0
let P be Probability of Sigma; :: thesis: (P * ASeq) . n >= 0
A1: n in NAT by ORDINAL1:def 12;
dom (P * ASeq) = NAT by SEQ_1:1;
then (P * ASeq) . n = P . (ASeq . n) by A1, FUNCT_1:12;
hence (P * ASeq) . n >= 0 by PROB_1:def 8; :: thesis: verum