Lemma multNonnegativeRationals_ltcompat_l : ∏ k x y : NonnegativeRationals, 0 < k -> (x < y) <-> (k * x < k * y). Proof. intros k x y Hk. split ; intro H. - apply (hqlthandmultl (pr1 x) (pr1 y) (pr1 k)). + exact Hk. + exact H. - apply (hqlthandmultlinv (pr1 x) (pr1 y) (pr1 k)). + exact Hk. + exact H. Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.Fields. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim.