Lemma NQmax_case : ∏ (P : NonnegativeRationals -> UU), ∏ x y : NonnegativeRationals, P x -> P y -> P (NQmax x y). Proof. intros P x y Hx Hy. unfold NQmax. generalize (isdecrel_leNonnegativeRationals x y). now apply coprod_rect. 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.