proposition: Lemma interval_cartesian_cubical_sets_two_elements : ∏ n : cartesian_cube_category, ∑ f g : ((I : functor _ _) n : hSet), f != g.
proof: Proof. intro n. exists (λ _ : stn 1, @inr (stn n) (stn 2) (make_stn 2 0 (idpath _))). exists (λ _ : stn 1, @inr (stn n) (stn 2) (make_stn 2 1 (idpath _))). intro p. apply toforallpaths in p. set (e := p (make_stn 1 0 (idpath _))). apply ii2_injectivity in e. apply (maponpaths pr1) in e. apply (negpaths0sx 0 e). Defined.
imports: UniMath.MoreFoundations.All UniMath.Combinatorics.FiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Presheaf UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.ExponentiationLeftAdjoint UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Structures