proposition: Lemma ratSubtract_add_same_l : forall r1 r2 r3, r1 <= r3 -> ratSubtract (r2 + r3) (r2 + r1) == ratSubtract r3 r1.
proof: Proof. intuition. unfold ratSubtract. rattac. arithNormalize. rewrite Nat.sub_add_distr. apply minus_eq_compat. rewrite Nat.add_comm. rewrite <- Nat.add_sub_assoc. rewrite minus_diag_eq. rewrite Nat.add_0_r. do 5 arithSimplify. do 5 arithSimplify. eapply le_eq. do 5 arithSimplify. do 5 arithSimplify. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms