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