Lemma disp_nat_z_iso_iso_inv {α: nat_z_iso F G} (β: disp_nat_z_iso DF DG α) (c:C) (d:D c) : (β c d) ;; (disp_nat_z_iso_to_trans_inv β c d) = transportb (mor_disp (DF c d) (DF c d)) (nat_z_iso_iso_inv α c d) (id_disp (DF c d)). Proof. etrans. apply (pr2 (pr2 (pr2 β c d))). apply two_arg_paths. - apply uip. apply homset_property. - reflexivity. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.