proposition: Theorem ratMult_nz : forall r1 r2, (~r1 * r2 == 0) <-> (~r1 == 0) /\ (~r2 == 0).
proof: Proof. intuition. eapply H. specialize (ratMult_0 r1 r2); intuition. eapply H. specialize (ratMult_0 r1 r2); intuition. apply ratMult_0 in H0. intuition. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms