Definition z_iso_disp_codomain {C : category} {x y : C} {f : z_iso x y} {h₁ : disp_codomain C x} {h₂ : disp_codomain C y} (g : z_iso (pr1 h₁) (pr1 h₂)) (p : g · pr2 h₂ = pr2 h₁ · f) : z_iso_disp f h₁ h₂. Proof. use make_z_iso_disp. - exact (pr1 g ,, p). - simple refine (_ ,, _ ,, _). + refine (inv_from_z_iso g ,, _). abstract (use z_iso_inv_on_right ; rewrite !assoc ; use z_iso_inv_on_left ; exact p). + abstract (use eq_cod_mor ; rewrite transportb_cod_disp ; cbn ; apply z_iso_after_z_iso_inv). + abstract (use eq_cod_mor ; rewrite transportb_cod_disp ; cbn ; 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.