proposition: Lemma cut_minus_le_trans x y z : y ≤ x → z ≤ y → (x ∸ y) + (y ∸ z) = x ∸ z.
proof: Proof. intros. apply (right_cancellation (+) z). rewrite <-associativity, !cut_minus_le; try easy. now transitivity y. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.additional_operations MathClasses.interfaces.orders MathClasses.orders.minmax