proposition: Lemma cut_minus_nonneg x y : 0 ≤ x ∸ y.
proof: Proof. destruct (total (≤) x y) as [E|E]. apply orders.eq_le. symmetry. now auto. apply (order_reflecting (+ y)). now rewrite cut_minus_le; ring_simplify. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.additional_operations MathClasses.interfaces.orders MathClasses.orders.minmax