Proposition iscontr_inequal (n m : nat) : iscontr ((n > m) ⨿ (n ≤ m)). Proof. unfold iscontr. exists (natgthorleh n m). intro t. induction t. - unfold natgthorleh. induction (isdecrelnatgth n m). + simpl. apply maponpaths. apply (pr2 (n > m)). + contradiction. - unfold natgthorleh. induction (isdecrelnatgth n m). + simpl. assert (¬ (n > m)). { apply natlehtonegnatgth. assumption. } contradiction. + simpl. apply maponpaths. apply (pr2 (n ≤ m)). Defined.
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.