Lemma ε_ses_ff_ax : disp_nat_trans_axioms ε_ses_ff_data. Proof. intros x y f xx yy ff. cbn. unfold ε_ses_ff_data. etrans. apply maponpaths_2; use homotweqinvweq. etrans. apply mor_disp_transportf_postwhisker. etrans. apply maponpaths. etrans. apply assoc_disp_var. apply maponpaths. etrans. apply maponpaths. apply (z_iso_disp_after_inv_mor (pr2 (FF_split _ _))). etrans. apply mor_disp_transportf_prewhisker. apply maponpaths, id_right_disp. etrans. apply transport_f_f. etrans. apply transport_f_f. etrans. apply transport_f_f. unfold transportb. apply maponpaths_2, homset_property. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. 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.Fiber.