Theorem unicity_univ_prop_reindexing_forward : ∏ DH' :disp_functor H D' D'', disp_nat_z_iso (disp_functor_composite DF DH') DG (nat_z_iso_id (F ∙ H)) -> disp_nat_z_iso DH' DH (nat_z_iso_id H). Proof. intros DH' µ'. apply DH0_DH1_disp_nat_z_iso. apply (transportf _ (comp_nat_z_iso_id_left (nat_z_iso_id (F ∙ H)))). apply (disp_nat_z_iso_comp µ'). apply (transportf _ nat_z_iso_inv_id). exact (disp_nat_z_iso_inv univ_prop_reindexing_forward). 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.