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
Prob.( (inferior_setsequence Complement A).n ) =
  1-Prob.( (superior_setsequence A).n )
  proof
A1: Prob.((inferior_setsequence Complement A).n) =
    Prob.((superior_setsequence A).n)` by Th9;
    Prob.((superior_setsequence A).n)` =
      Prob.( ([#] Sigma) \ (superior_setsequence A).n) by SUBSET_1:def 4;
    hence thesis by A1,PROB_1:32;
  end;
