proposition: Lemma Zmod_opp_nonzero : forall m a : Z, (m > 0)%Z -> (a mod m)%Z <> 0%Z -> (- a mod m)%Z = (m - a mod m)%Z.
proof: Proof. intros m a Hm Ha. rewrite (Zmod_opp_elim m a Hm). apply Zmod_small. exact Hm. generalize (Z_mod_lt a m Hm); intro Hlt. auto with zarith. Qed.
imports: CoRN.model.Zmod.ZGcd