proposition: Lemma neg_pos_mult x y : x < 0 → 0 < y → x * y < 0.
proof: Proof. intros. rewrite <-(mult_0_r x). now apply flip_neg_mult_l. Qed.
imports: Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.theory.rings MathClasses.orders.orders MathClasses.orders.maps