proposition: Lemma nonneg_nonpos_mult x y : 0 ≤ x → y ≤ 0 → x * y ≤ 0.
proof: Proof. intros. rewrite commutativity. now apply nonpos_nonneg_mult. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps