proposition: Lemma pos_neg_mult x y : 0 < x -> y < 0 -> x * y < 0.
proof: Proof. intros. rewrite (commutativity (f:=mult)). apply neg_pos_mult;trivial. Qed.
imports: HoTT.Classes.theory.apartness HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.rings HoTT.Classes.orders.orders HoTT.Classes.orders.maps