Lemma multNonnegativeRationals_lecompat_l : ∏ k x y : NonnegativeRationals, x <= y -> k * x <= k * y. Proof. intros k x y Hle. generalize (eq0orgt0NonnegativeRationals k) ; apply sumofmaps ; intros Hk0. - rewrite Hk0. rewrite !islabsorb_zero_multNonnegativeRationals. now apply isrefl_leNonnegativeRationals. - apply hqlehandmultl, Hle. exact Hk0. 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.