
theorem for a be even Integer holds a div 2 = (a+1) div 2
  proof
    let a be even Integer;
    ((a+1) div 2)*2 + ((a+1) mod 2) = a + 1 by INT_1:59
    .= (a div 2)*2 + (a mod 2) + 1 by INT_1:59
    .= (a div 2)*2 + ((a+1) mod 2);
    hence thesis;
  end;
