proposition: Lemma cut_minus_negate (x : R) : x ≤ 0 → 0 ∸ x = -x.
proof: Proof. intros. now rewrite <-(rings.plus_0_l (-x)), cut_minus_ring_minus. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.additional_operations MathClasses.interfaces.orders MathClasses.orders.minmax