Definition disp_inv2cell_to_disp_z_iso : disp_invertible_2cell (id2_invertible_2cell f) ff₁ ff₂ → @z_iso_disp _ (disp_hom xx yy) _ _ (identity_z_iso _) ff₁ ff₂. Proof. intro α. simple refine (@make_z_iso_disp _ (disp_hom xx yy) _ _ _ _ _ _ _). - exact (pr1 α). - simple refine (_ ,, _ ,, _). + exact (disp_inv_cell α). + abstract (refine (disp_vcomp_linv α @ _) ; cbn ; apply maponpaths_2 ; apply cellset_property). + abstract (refine (disp_vcomp_rinv α @ _) ; cbn ; apply maponpaths_2 ; apply cellset_property). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations.