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 *)

Theorem div_mod_unique : forall b q1 q2 r1 r2 : t,
0<=r1<abs b -> 0<=r2<abs b ->
b*q1+r1 == b*q2+r2 -> q1 == q2 /\ r1 == r2.