proposition: Lemma ratSubtract_0 : forall r1 r2, r1 <= r2 -> ratSubtract r1 r2 == 0.
proof: Proof. intuition. unfold ratSubtract. rattac. inversion l; clear l; subst. lia. rewrite H0. unfold posnatToNat in *. lia. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms