(** Cancellations. *)
(** With the current convention, the following isn't always true when [c<0]: [-3*-1 / -2*-1 = 3/2 = 1] while [-3/-2 = 2] *)

Lemma mul_mod_distr_r: forall a b c, b~=0 -> 0<c ->
(a*c) mod (b*c) == (a mod b) * c.