proposition: Lemma flip_neg_mult_r x y z : z < 0 -> x < y -> y * z < x * z.
proof: Proof. rewrite 2!(commutativity _ z). apply flip_neg_mult_l. 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