reserve x, y for set;

theorem
  for a being Integer holds round a = a
  proof
    let a be Integer;
    a - 1/2 < a - 0 by XREAL_1:6; then
    a + (0 qua Nat) <= a + 1/2 & a + 1/2 - 1 < a - 0 by XREAL_1:6;
    hence thesis by INT_1:def 6;
  end;
