proposition: Lemma rem_nonneg : forall a b, b~=0 -> 0 <= a -> 0 <= a rem b.
proof: Proof. intros a b **. pos_or_neg b. - destruct (rem_bound_pos a b); order. - rewrite <- rem_opp_r; trivial. destruct (rem_bound_pos a (-b)); trivial. Qed.
imports: ZAxioms ZMulOrder ZSgnAbs NZDiv