Lemma NRNRtoR_zero : NRNRtoR 0%NR 0%NR = 0. Proof. unfold NRNRtoR, NR_to_hr. refine (setquotl0 _ 0 (_,,_)). apply hinhpr. exists 0%NR ; simpl. reflexivity. 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.