reserve Omega, Omega1, Omega2 for non empty set;
reserve Sigma for SigmaField of Omega;
reserve S1 for SigmaField of Omega1;
reserve S2 for SigmaField of Omega2;
reserve F for random_variable of S1,S2;

theorem Th14:
  for P being Probability of S1,
  F be random_variable of S1,S2 holds
  for y be set st y in S2 holds (probability(F,P)).y = P.(F"y)
  proof
    let P be Probability of S1, F be random_variable of S1,S2;
    let y be set;
    assume A1: y in S2;
    thus (probability(F,P)).y = (image_measure(F,P2M(P))).y by Th13
    .= P.(F"y) by A1,Def6;
  end;
