proposition: Lemma nonneg_nonpos_mult x y : 0 ≤ x -> y ≤ 0 -> x * y ≤ 0.
proof: Proof. intros. rewrite (commutativity (f:=mult)). apply nonpos_nonneg_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