Definition from_is_disp_invertible_2cell_cod {B : bicat} {X Y : B} {f g : X --> Y} {α : invertible_2cell f g} {dX : cod_disp_bicat B X} {dY : cod_disp_bicat B Y} {ff : dX -->[ f ] dY} {gg : dX -->[ g ] dY} (αα : ff ==>[ α ] gg) (Hαα : is_disp_invertible_2cell α αα) : is_invertible_2cell (pr1 αα). Proof. use make_is_invertible_2cell. - exact (pr11 Hαα). - abstract (exact (maponpaths pr1 (pr12 Hαα) @ transportb_cell_of_cod_over _ _)). - abstract (exact (maponpaths pr1 (pr22 Hαα) @ transportb_cell_of_cod_over _ _)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. 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.Examples.OneTypes. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Trivial. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma.