Definition disp_z_iso_to_disp_inv2cell : @z_iso_disp _ (disp_hom xx yy) _ _ (identity_z_iso _) ff₁ ff₂ → disp_invertible_2cell (id2_invertible_2cell f) ff₁ ff₂. Proof. intro α. simple refine (_ ,, _ ,, _ ,, _). - exact (pr1 α). - exact (inv_mor_disp_from_z_iso α). - abstract (cbn ; refine (pr222 α @ _) ; apply maponpaths_2 ; apply cellset_property). - abstract (cbn ; refine (pr122 α @ _) ; 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.