proposition: Lemma cut_minus_le_r x y : y ≤ x → x ∸ y + y = x.
proof: Proof. Proof cut_minus_le x y. Lemma cut_minus_le_l x y : y ≤ x → y + (x ∸ y) = x. Proof. rewrite commutativity. now apply cut_minus_le. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.additional_operations MathClasses.interfaces.orders MathClasses.orders.minmax