
theorem
  for a,b being Real st a < b holds (a+b)/2 < b
  proof
    let a,b be Real;
    assume a < b;
    then a + b < b + b by XREAL_1:8;
    then (a+b)/2 < 2 * b / 2 by XREAL_1:74;
    hence thesis;
  end;
