(** The sign of [a mod b] is the one of [b] (when it isn't null) *)

(** NB: The four previous properties could be used as specifications for [div]. *)
(** Inequality [mul_div_le] is exact iff the modulo is zero. *)
Lemma div_exact : forall a b, b~=0 -> (a == b*(a/b) <-> a mod b == 0).