theorem Th15:
  P.A + P.B - 1 <= P.(A /\ B)
proof
  P.A + P.B - P.(A /\ B) = P.(A \/ B) by PROB_1:38;
  then P.A + P.B - P.(A /\ B) <= 1 by PROB_1:35;
  then P.A + P.B <= P.(A /\ B) + 1 by XREAL_1:20;
  hence thesis by XREAL_1:20;
end;
