Lemma hr_mult_ltcompat_r' : ∏ x y z : hr_commring, hr_le_rel 0%ring x -> hr_lt_rel (x * y)%ring (x * z)%ring -> hr_lt_rel y z. Proof. intros x y z. rewrite !(ringcomm2 _ x). apply hr_mult_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.