Lemma hr_to_NR_bij : ∏ x : hr_commring, NR_to_hr (hr_to_NR x) = x. Proof. intros x. unfold NR_to_hr. pattern x at 2. apply (setquotl0 _ x ((hr_to_NR x),,(hr_to_NR_correct x))). 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.