Lemma DH0_DH1_nat_trans_axioms {DH0 DH1 :disp_functor H D' D''} (β: disp_nat_trans (nat_z_iso_id (F ∙ H)) (DF ◦ DH0) (DF ◦ DH1)) : disp_nat_trans_axioms (DH0_DH1_nat_trans_data β). Proof. intros a' b' f' x' y' Df'. induction x' as (a,(px,x)). induction y' as (b,(py,y)). induction Df' as (f,(pf,Df)). destruct px, py, pf. cbn. etrans. apply (pr2 β a b f x y Df). apply two_arg_paths. - apply uip. apply homset_property. - reflexivity. Qed.
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.