theorem
  (O1 OR O2) AND NOT O1 c= O2
  proof
    (O1 OR O2) AND NOT O1 = (O1 AND NOT O1)OR (O2 AND NOT O1) by XBOOLE_1:23
    .= {} \/ (O2 AND NOT O1) by Th52
    .= O2 AND NOT O1;
    hence thesis by XBOOLE_1:17;
  end;
