Lemma NRNRtoR_RtoNRNR : ∏ x : Reals, NRNRtoR (pr1 (RtoNRNR x)) (pr2 (RtoNRNR x)) = x. Proof. intros X. unfold NRNRtoR. apply hr_to_NR_bij. 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.