Module Import Private_NZDiv := Nop <+ NZDivProp N N NP.
Ltac auto' := try rewrite <- neq_0_lt_0; auto using le_0_l.
(** Let's now state again theorems, but without useless hypothesis. *)
(** Uniqueness theorems *)

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