Lemma plusNonnegativeRationals_le_lt_ltcompat : ∏ x x' y y' : NonnegativeRationals, x <= x' -> y < y' -> x + y < x' + y'. Proof. intros x x' y y' Hx Hy. apply istrans_lt_le_ltNonnegativeRationals with (x + y'). - now apply hqlthandplusl, Hy. - now apply hqlehandplusr, Hx. 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.