Lemma DH0_DH1_nat_trans_data {DH0 DH1:disp_functor H D' D''} (β: disp_nat_trans (nat_z_iso_id (F ∙ H)) (DF ◦ DH0) (DF ◦ DH1)) :disp_nat_trans_data (nat_z_iso_id H) DH0 DH1. Proof. intros c' d'. apply (DF_inv_mor DH0 DH1 c' d'). exact (β ↙d' ←d'). 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.