 reserve U for set,
         X, Y for Subset of U;
 reserve U for non empty set,
         A, B, C for non empty IntervalSet of U;

theorem
  (Inter ([#]U,[#]U))^ = Inter ({}U,{}U)
  proof
    (Inter ([#]U,[#]U))^ = Inter (([#]U)`,([#]U)`) by Th46
      .= Inter ({}U,([#]U)`) by XBOOLE_1:37;
    hence thesis by XBOOLE_1:37;
  end;
