Lemma plusNonnegativeRationals_ltcompat_l : ∏ x y z : NonnegativeRationals, (y < z) <-> (x + y < x + z). Proof. intros x y z. rewrite !(iscomm_plusNonnegativeRationals x). now apply plusNonnegativeRationals_ltcompat_r. Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.RealNumbers.Sets. Require Import UniMath.RealNumbers.Fields. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.RealNumbers.Prelim.