proposition: Proposition iscontr_inequal (n m : nat) : iscontr ((n > m) ⨿ (n ≤ m)).
proof: 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.
imports: UniMath.Foundations.PartD UniMath.Foundations.NaturalNumbers UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.FiniteSets UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsTensored UniMath.CategoryTheory.SimplicialSets