
theorem
  for X being set holds X \/ {} = X
proof
  let X be set;
  thus X \/ {} c= X
  proof
    let x be object;
    assume x in X \/ {};
    then x in X or x in {} by XBOOLE_0:def 3;
    hence thesis by XBOOLE_0:def 1;
  end;
  let x be object;
  assume x in X;
  hence thesis by XBOOLE_0:def 3;
end;
