Lemma two_cat_is_strict_bicat (C : two_cat) : is_strict_bicat (two_cat_to_bicat C). Proof. use make_is_strict_bicat. - apply (homset_property C). - use tpair. + repeat split. * intros a b f. exact (id_left (f : pr1 C ⟦ _ , _ ⟧)). * intros a b f. exact (id_right (f : pr1 C ⟦ _ , _ ⟧)). * intros a b c d f g h. exact (assoc (f : pr1 C ⟦ _ , _ ⟧) g h). + simpl. repeat split ; intros ; apply idto2mor_idtoiso_two_cat. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.TwoCategories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.TransportLaws.