theorem Th31:
  P.(([#] Sigma) \ A) + P.A = 1
proof
A1: (([#] Sigma) \ A) \/ A = A` \/ A .= [#] Omega by SUBSET_1:10
    .= Omega;
  (([#] Sigma) \ A) misses A by XBOOLE_1:79;
  then P.(([#] Sigma) \ A) + P.A = P.Omega by A1,Def8
    .= 1 by Def8;
  hence thesis;
end;
