Definition disp_map_slice_biinitial_1cell_property : biinitial_1cell_property disp_map_slice_biinitial_obj. Proof. intros h. simple refine (_ ,, _ ,, _). - exact (is_biinitial_1cell_property (pr2 I) (pr1 h)). - exact (pr2 HD _ _ (pr12 h)). - use make_invertible_2cell ; cbn. + apply (is_biinitial_2cell_property (pr2 I)). + use make_is_invertible_2cell. * apply (is_biinitial_2cell_property (pr2 I)). * apply (is_biinitial_eq_property (pr2 I)). * apply (is_biinitial_eq_property (pr2 I)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayMapBicatSlice. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Logic.DisplayMapBicat.