proposition: Lemma ratInverse_1_swap : forall r, ~ r == 0 -> r <= 1 -> 1 <= ratInverse r.
proof: Proof. intuition. unfold ratInverse. destruct r. destruct n. exfalso. eapply H. eapply rat_num_0. rattac. inversion H1; clear H1; subst. lia. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms