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;
