Definition inv_disp_from_pointwise_z_iso (x y : FunctorsC'C) (f : z_iso x y) (xx : disp_functor_cat x) (yy : disp_functor_cat y) (FF : xx -->[ f ] yy) (H : forall x' (xx' : D' x') , is_z_iso_disp (pointwise_z_iso_from_nat_z_iso f _ ) (pr1 FF _ xx' )) : yy -->[ inv_from_z_iso f] xx. Proof. use tpair. + intros x' xx'. exact (inv_mor_disp_from_z_iso (H x' xx')). + intros x' x0 f0 xx' xx0 ff. apply is_disp_nat_trans_pointwise_inv. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.