proposition: Lemma nonpos_nonneg_mult x y : x ≤ 0 -> 0 ≤ y -> x * y ≤ 0.
proof: Proof. intros. rewrite <-(mult_0_r x). apply flip_nonpos_mult_l;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