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. *)

Lemma mod_1_r: forall a, a mod 1 == 0.