Lemma Rabs_pr2RtoNRNR : ∏ x : Reals, (pr2 (RtoNRNR x) <= Rabs x)%NR. Proof. intros x. rewrite <- (NRNRtoR_RtoNRNR x). generalize (pr1 (RtoNRNR x)) (pr2 (RtoNRNR x)) ; clear x ; intros x y ; simpl. apply maxNonnegativeReals_le_r. 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.