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 Th17:
  for V,S be finite non empty set,
  G be random_variable of Trivial-SigmaField (V),Trivial-SigmaField (S)
  holds
  for y be set st y in Trivial-SigmaField (S) holds
  (probability(G,Trivial-Probability V)).y = card(G"y)/card(V)
  proof
    let V,S be finite non empty set,
    G be random_variable of Trivial-SigmaField (V),Trivial-SigmaField (S);
    now let y be set;
      assume A1: y in Trivial-SigmaField (S);
      thus (probability(G,Trivial-Probability (V))).y
       = (Trivial-Probability (V)).(G"y) by Th14,A1
      .= prob(G"y) by RANDOM_1:def 1
      .= card(G"y)/card (V);
    end;
    hence thesis;
  end;
