proposition: Lemma ratSubtract_le_sum : forall r1 r2 d, r2 <= r1 -> ratSubtract r1 r2 <= d -> r1 <= r2 + d.
proof: Proof. intuition. rewrite <- (ratSubtract_ratAdd_inverse r2). rewrite ratSubtract_ratAdd_assoc. eapply ratAdd_leRat_compat; eauto. intuition. trivial. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms