Definition disp_cell_unit_bicat_idtoiso {a b : C} (p : a = b) (aa : disp_cell_unit_bicat a) (bb : disp_cell_unit_bicat b) : transportf disp_cell_unit_bicat p aa = bb → (aa -->[ idtoiso_2_0 _ _ p ] bb) × (bb -->[ left_adjoint_right_adjoint (idtoiso_2_0 _ _ p)] aa). Proof. induction p ; cbn. intros pp. induction pp ; cbn. split ; apply id_disp. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. 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.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.