Module Import Private_NZDiv := Nop <+ NZDivProp A D B.
(** Another formulation of the main equation *)
Ltac pos_or_neg a :=
let LT := fresh "LT" in
let LE := fresh "LE" in
destruct (le_gt_cases 0 a) as [LE|LT]; [|rewrite <- opp_pos_neg in LT].
(** Uniqueness theorems *)
(** Sign rules *)
(** A division by itself returns 1 *)
(** A division of a small number by a bigger one yields zero. *)
(** * Order results about mod and div *)
(** A modulo cannot grow beyond its starting point. *)

Theorem mod_le: forall a b, 0<=a -> b~=0 -> a mod b <= a.