proposition: Lemma ge_1_mult_le_compat_r x y z : 1 ≤ z -> 0 ≤ y -> x ≤ y -> x ≤ y * z.
proof: Proof. intros. transitivity y; [trivial |]. pattern y at 1;apply (transport _ (mult_1_r y)). apply (order_preserving_nonneg (.*.) y);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