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 *)

Lemma mod_opp_opp_nz : forall a b, b~=0 -> a mod b ~= 0 ->
(-a) mod (-b) == abs b - a mod b.