Lemma hr_to_NR_one : hr_to_NR 1%ring = (1,,0). Proof. unfold ringunel2, unel_is ; simpl. unfold rigtoringunel2, hr_to_NR. rewrite setquotunivcomm ; simpl. erewrite <- minusNonnegativeReals_correct_r. - rewrite minusNonnegativeReals_eq_zero. + reflexivity. + apply isnonnegative_NonnegativeReals. - apply pathsinv0, isrunit_zero_plusNonnegativeReals. 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.