
theorem Th2:
  for X, Y, Z being set holds X /\ Z misses Y \ Z
proof
  let X, Y, Z be set;
  (X /\ Z) /\  (Y \ Z) = X /\ (Z /\ (Y \ Z)) by XBOOLE_1:16
    .= X /\ ((Z /\ Y) \ (Z /\ Z)) by XBOOLE_1:50
    .= X /\ {} by XBOOLE_1:17, XBOOLE_1:37
    .= {};
  hence thesis by XBOOLE_0:def 7;
end;
