(** Similarly, the following result doesn't always hold when [c<0]. For instance [3 mod (-2*-2)) = 3] while [3 mod (-2) + (-2)*((3/-2) mod -2) = -1]. *)

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