Lemma hr_lt_le : ∏ X Y, hr_lt_rel X Y -> hr_le_rel X Y. Proof. intros x y. rewrite <- (hr_to_NR_bij x), <- (hr_to_NR_bij y). intro H. apply NR_to_hr_le. apply lt_leNonnegativeReals. apply_pr2 NR_to_hr_lt. exact H. 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.