Definition transportf_disp_2cell {B : bicat} {D : disp_bicat B} {x y : B} {f g : x --> y} {xx : D x} {yy : D y} (ff : xx -->[ f ] yy) (p : f = g) : disp_invertible_2cell (idtoiso_2_1 _ _ p) ff (transportf _ p ff). Proof. induction p. cbn. exact (disp_id2_invertible_2cell ff). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor.