proposition: Lemma flip_nonpos_mult_r x y z : z ≤ 0 → x ≤ y → y * z ≤ x * z.
proof: Proof. rewrite 2!(commutativity _ z). now apply flip_nonpos_mult_l. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps