proposition: Lemma flip_nonpos_mult_r x y z : z ≤ 0 -> x ≤ y -> y * z ≤ x * z.
proof: Proof. rewrite 2!(commutativity _ z). apply flip_nonpos_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