Definition transportf_disp_invertible_2cell {B : bicat} {D : disp_bicat B} {x y : B} {f g : x --> y} {xx : D x} {yy : D y} {ff : xx -->[ f ] yy} {gg : xx -->[ g ] yy} {α β : invertible_2cell f g} (p : α = β) (αα : disp_invertible_2cell α ff gg) : pr1 (transportf (λ (z : invertible_2cell f g), disp_invertible_2cell z ff gg) p αα) = transportf (λ z, ff ==>[ z ] gg) (maponpaths pr1 p) αα.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells.