Lemma DH0_DH1_disp_nat_z_iso {DH0 DH1 :disp_functor H D' D''} (β: disp_nat_z_iso (DF ◦ DH0) (DF ◦ DH1) (nat_z_iso_id (F ∙ H))) : disp_nat_z_iso DH0 DH1 (nat_z_iso_id H). Proof. use tpair. - exact (DH0_DH1_nat_trans β). - apply DH0_DH1_is_disp_nat_z_iso. 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.