proposition: Theorem ratSubtract_leRat_same_r : forall r1 r2 r3, r3 <= r1 -> r3 <= r2 -> ratSubtract r1 r3 <= ratSubtract r2 r3 -> r1 <= r2.
proof: Proof. intuition. apply (ratAdd_leRat_compat_l r3) in H1. assert (ratSubtract r1 r3 + r3 == r1). rewrite ratAdd_comm. eapply ratSubtract_ratAdd_inverse_2; intuition. rewrite <- H2. rewrite H1. rewrite ratAdd_comm. eapply eqRat_impl_leRat. apply ratSubtract_ratAdd_inverse_2; intuition. Qed.
imports: FCF.Crypto FCF.Bernoulli FCF.NotationV1