proposition: Lemma ratInverse_leRat : forall r1 r2, ~ r2 == 0 -> r2 <= r1 -> ratInverse r1 <= ratInverse r2.
proof: Proof. intuition. unfold ratInverse. rattac. destruct n0. exfalso. eapply H. eapply rat_num_0. destruct n. exfalso. rewrite Nat.mul_0_l in l. simpl in *. remember (n0 * x1)%nat as a. nia. inversion H3; clear H3; subst. inversion H2; clear H2; subst. nia. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms