proposition: Lemma mod_opp_r : forall a b, b~=0 -> a mod (-b) == a mod b.
proof: Proof. intros. symmetry. apply mod_unique with (-(a/b)). - rewrite abs_opp; now apply mod_always_pos. - rewrite mul_opp_opp; now apply div_mod. Qed.
imports: ZAxioms ZMulOrder ZSgnAbs NZDiv