Lemma iscomm_NQmax : ∏ x y, NQmax x y = NQmax y x. Proof. intros x y. apply NQmax_case_strong ; intro Hle ; apply NQmax_case_strong ; intro Hle'. - now apply isantisymm_leNonnegativeRationals. - reflexivity. - reflexivity. - now apply isantisymm_leNonnegativeRationals. 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.