proposition: Lemma nonpos_mult x y : x ≤ 0 → y ≤ 0 → 0 ≤ x * y.
proof: Proof. intros. rewrite <-(mult_0_r x). 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