Definition data_functor_univ_prop_reindexing_forward : disp_functor_data H D' D''. Proof. use tpair. - intros c' d'. exact (transportf (λ x, D'' (H x)) (¤ d') (DG (↙ d') (← d'))). - intros a' b' x' y' f' Df'. apply (transportf (λ f0, mor_disp _ _ (# H f0)) (¤ Df')). apply double_transport_disp. exact ((♯ DG (← Df'))%mor_disp). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.StreetFibration.