(** * Relations between usual operations and mod and div *)

(* Specifications: *)
Lemma mod_add : forall a b c, 0<=a -> 0<=a+b*c -> 0<c ->
(a + b * c) mod c == a mod c.
Lemma div_add : forall a b c, 0<=a -> 0<=a+b*c -> 0<c ->
(a + b * c) / c == a / c + b.
Lemma div_add_l: forall a b c, 0<=c -> 0<=a*b+c -> 0<b ->
(a * b + c) / b == a + c / b.