Definition inverse_of_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 : disp_invertible_2cell α ff gg) : disp_invertible_2cell (inv_of_invertible_2cell α) gg ff. Proof. simple refine (_ ,, _). - exact (disp_inv_cell αα). - exact (disp_inv_cell_is_disp_invertible_2cell (pr2 αα)). 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.