Definition natlthorgeh_right_branch {n m : nat} (s : n ≥ m) (j : (n < m) ⨿ (n ≥ m)) : j = inr s := (proofirrelevancecontr (iscontr_inequal m n) j (inr s)).
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.FiniteSets. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored. Require Import UniMath.CategoryTheory.SimplicialSets.