let Omega be non empty set ; :: thesis: for Sigma being SigmaField of Omega
for P being Probability of Sigma
for A, B being non empty Subset of Sigma st A c= Indep (B,P) holds
B c= Indep (A,P)
let Sigma be SigmaField of Omega; :: thesis: for P being Probability of Sigma
for A, B being non empty Subset of Sigma st A c= Indep (B,P) holds
B c= Indep (A,P)
let P be Probability of Sigma; :: thesis: for A, B being non empty Subset of Sigma st A c= Indep (B,P) holds
B c= Indep (A,P)
let A, B be non empty Subset of Sigma; :: thesis: ( A c= Indep (B,P) implies B c= Indep (A,P) )
assume A1: A c= Indep (B,P) ; :: thesis: B c= Indep (A,P)
for q, p being Event of Sigma st q in B & p in A holds
q,p are_independent_respect_to P by A1, Th7, PROB_2:19;
hence B c= Indep (A,P) by Th7; :: thesis: verum