Lemma Rabs_Ropp : ∏ x : Reals, (Rabs (- x)%R = Rabs x). Proof. intros x. rewrite <- (NRNRtoR_RtoNRNR x). apply iscomm_maxNonnegativeReals. 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.