Lemma NQmax_case_strong : ∏ (P : NonnegativeRationals -> UU), ∏ x y : NonnegativeRationals, (y <= x -> P x) -> (x <= y -> P y) -> P (NQmax x y). Proof. intros P x y Hx Hy. unfold NQmax. generalize ( isdecrel_leNonnegativeRationals x y). apply coprod_rect ; [intros Hle | intros Hlt]. - now apply Hy. - apply Hx. now apply lt_leNonnegativeRationals, notge_ltNonnegativeRationals. 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.