(** A division by itself returns 1 *)

(** In this convention, [div] performs Rounding-Toward-Bottom when divisor is positive, and Rounding-Toward-Top otherwise.  Since we cannot speak of rational values here, we express this fact by multiplying back by [b], and this leads to a nice unique statement. *)
Lemma mul_div_le : forall a b, b~=0 -> b*(a/b) <= a.