proposition: Lemma cat_not_a_two_cat : ¬ (is_strict_bicat bicat_of_univ_cats).
proof: Proof. intro H. pose (maponpaths pr1 (eqtohomot (nat_trans_eq_pointwise (maponpaths (λ z, pr1 z) (proofirrelevance _ (@univalent_two_cat_2cells_are_prop (bicat_of_univ_cats ,, H) univalent_cat_is_univalent_2_1 HSET_univalent_category HSET_univalent_category diag_set diag_set) (id2_invertible_2cell _) (nat_z_iso_to_invertible_2cell _ _ swap))) boolset) (true ,, false))) as C. exact (nopathstruetofalse C). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.TwoCategories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Categories.HSET.All UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.TransportLaws