Lemma hr_abs_minus : ∏ x y : hr_ConstructiveField, hr_abs x - hr_abs y <= hr_abs (x - y)%ring. Proof. intros x y. rewrite <- (hr_abs_opp y). apply istriangle_hr_abs'. 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.