Lemma hr_plus_lecompat_r : ∏ x y z : hr_commring, hr_le_rel y z <-> hr_le_rel (x + y)%ring (x + z)%ring. Proof. intros x y z. rewrite !(ringcomm1 _ x). apply hr_plus_lecompat_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.