Definition disp_inv_cell_is_disp_invertible_2cell {B : bicat} {D : disp_bicat B} {x y : B} {f g : x --> y} {α : invertible_2cell f g} {xx : D x} {yy : D y} {ff : xx -->[ f ] yy} {gg : xx -->[ g ] yy} {αα : ff ==>[ α ] gg} (Hαα : is_disp_invertible_2cell α αα) : is_disp_invertible_2cell (is_invertible_2cell_inv α) (disp_inv_cell (αα ,, Hαα)). Proof. refine (αα ,, _ ,, _). - exact (disp_vcomp_linv (αα ,, Hαα)). - exact (disp_vcomp_rinv (αα ,, Hαα)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells.