Definition make_disp_map_disp_invertible_2cell {x y : B} {f g : x --> y} {γ : f ==> g} (Hγ : is_invertible_2cell γ) {hx : disp_map_bicat_to_disp_bicat x} {hy : disp_map_bicat_to_disp_bicat y} {hf : hx -->[ f ] hy} {hg : hx -->[ g ] hy} (hγ : hf ==>[ γ ] hg) (Hhγ : is_invertible_2cell (pr1 hγ)) : disp_invertible_2cell (make_invertible_2cell Hγ) hf hg. Proof. refine (hγ ,, _). use is_invertible_to_is_disp_invertible. exact Hhγ. 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.CategoryTheory.DisplayedCats.StreetFibration. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.InternalStreetFibration. Require Import UniMath.Bicategories.Morphisms.InternalStreetOpFibration. Require Import UniMath.Bicategories.Logic.DisplayMapBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Codomain. Require Import UniMath.Bicategories.Limits.Pullbacks.