Definition iso_to_disp_iso (h : z_iso y z) (p : f = h · g) : z_iso_disp (identity_z_iso x) fy gz. Proof. use make_z_iso_disp. - refine (pr1 h ,, _). abstract (cbn ; rewrite id_right ; exact (!p)). - simple refine (_ ,, _ ,, _). + refine (inv_from_z_iso h ,, _). abstract (cbn ; rewrite id_right ; use z_iso_inv_on_right ; exact p). + abstract (use eq_cod_mor ; rewrite transportb_cod_disp ; apply z_iso_after_z_iso_inv). + abstract (use eq_cod_mor ; rewrite transportb_cod_disp ; apply z_iso_inv_after_z_iso). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations.