Lemma disp_functor_ff_inv_identity {x : C} (xx : D x) : disp_functor_ff_inv (transportb _ (functor_id F _ ) (id_disp (FF _ xx))) = id_disp xx. Proof. apply invmap_eq. apply pathsinv0. apply (disp_functor_id FF). Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.