Definition z_iso_disp_from_op_disp_cat {C : category} {D : disp_cat C} {x : C} {xx yy : D x} (f : @z_iso_disp _ (op_disp_cat D) _ _ (@identity_z_iso C^op x) xx yy) : z_iso_disp (identity_z_iso x) xx yy. Proof. use make_z_iso_disp. - exact (inv_mor_disp_from_z_iso f). - simple refine (_ ,, _ ,, _). + exact (pr1 f). + abstract (cbn ; refine (z_iso_disp_after_inv_mor f @ _) ; apply maponpaths_2 ; apply homset_property). + abstract (cbn ; refine (inv_mor_after_z_iso_disp f @ _) ; apply maponpaths_2 ; apply homset_property). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.