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 Th50:
  dom(O OR NOT O) = X
  proof
    thus dom(O OR NOT O) = (dom O) OR dom NOT O by XTUPLE_0:23
    .= (dom O) \/ dom id (X\dom O) by Th37
    .= (dom O) OR (X\dom O) by RELAT_1:45
    .= (dom O) \/ X by XBOOLE_1:39
    .= X by XBOOLE_1:12;
  end;
