proposition: Lemma ratSubtract_sum_1 : forall r1 r2, ~ r1 <= r2 -> r2 + (ratSubtract r1 r2) == r1.
proof: Proof. intuition. rewrite <- ratSubtract_ratAdd_assoc. eapply ratSubtract_ratAdd_inverse. apply bleRat_total. case_eq (bleRat r1 r2); intuition. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms