Module Import Private_NZDiv := Nop <+ NZDivProp A A B.
(** Another formulation of the main equation *)
(** We have a general bound for absolute values *)
(** Uniqueness theorems *)
Fact opp_mod_bound_or : forall a b, b~=0 ->
0 <= -(a mod b) < -b \/ -b < -(a mod b) <= 0.

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