Definition is_invertible_2cell_in_slice_bicat {B : bicat} {b : B} {f₁ f₂ : slice_bicat b} {g₁ g₂ : f₁ --> f₂} {α : g₁ ==> g₂} (Hα : is_invertible_2cell (pr1 α)) : is_invertible_2cell α. Proof. use is_invertible_disp_to_total. simple refine (_ ,, _). - exact Hα. - apply (disp_locally_groupoid_slice_disp_bicat _ _ _ _ _ (make_invertible_2cell Hα)). 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.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.