proposition: Lemma ratInverse_involutive : forall r, ~ r == 0 -> ratInverse (ratInverse r) == r.
proof: Proof. intuition. unfold ratInverse. destruct r. destruct n. exfalso. eapply H. eapply rat_num_0. destruct p. unfold posnatToNat, natToPosnat. destruct x. lia. eapply eqRat_terms; intuition. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms