reserve X,Y,z,s for set, L,L1,L2,A,B for List of X, x for Element of X,
  O,O1,O2,O3 for Operation of X, a,b,y for Element of X, n,m for Nat;
reserve F,F1,F2 for filtering Operation of X;

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;
