proposition: Lemma nonneg_mult_rev_l x y : 0 ≤ x * y -> 0 < y -> 0 ≤ x.
proof: Proof. intros. apply (order_reflecting (.* y)). rewrite rings.mult_0_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