Lemma Rmult_ltcompat_r: ∏ x y z : Reals, 0 < x -> y < z -> (x * y) < (x * z). Proof. intros x y z. rewrite !(iscomm_CFmult x). now apply Rmult_ltcompat_l. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.NonnegativeRationals.