reserve Omega for non empty set,
        Sigma for SigmaField of Omega,
        Prob for Probability of Sigma,
        A for SetSequence of Sigma,
        n,n1,n2 for Nat;

theorem Th8:
  Prob.( (Partial_Intersection Complement A).n ) =
  1-Prob.( (Partial_Union A).n )
proof
A1: Prob.((Partial_Intersection Complement A).n) =
  Prob.((Partial_Union A).n)` by Th7;
Prob.((Partial_Union A).n)` = Prob.( ([#] Sigma) \ (Partial_Union A).n)
 by SUBSET_1:def 4;
hence thesis by A1,PROB_1:32;
end;
