theorem Th14:
  C = B` implies P.A = P.(A /\ B) + P.(A /\ C)
proof
  assume
A1: C = B`;
  then B misses C by SUBSET_1:24;
  then A /\ C misses B by XBOOLE_1:74;
  then
A2: A /\ B misses A /\ C by XBOOLE_1:74;
  P.A = P.(A /\ [#]Omega) by XBOOLE_1:28
    .= P.(A /\ (B \/ C)) by A1,SUBSET_1:10
    .= P.(A /\ B \/ A /\ C) by XBOOLE_1:23
    .= P.(A /\ B) + P.(A /\ C) by A2,PROB_1:def 8;
  hence thesis;
end;
