proposition: Lemma cut_minus_min2 x y z : y ∸ z + ((y ⊓ z) ∸ x) = y ∸ x + ((x ⊓ y) ∸ z).
proof: Proof. rewrite <-cut_minus_min1. rewrite (commutativity x y), <-cut_minus_min1. now rewrite commutativity. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.additional_operations MathClasses.interfaces.orders MathClasses.orders.minmax