Definition is_z_iso_disp_transportb_fun_eq {C : category} {D : disp_cat C} {x y : C} (f : z_iso x y) {g : z_iso x y} {xx : D x} {yy : D y} (ff : xx -->[ f ] yy) (p : pr1 g = pr1 f) (Hff : is_z_iso_disp f ff) : is_z_iso_disp g (transportb (λ z, _ -->[ z ] _) p ff). Proof. apply is_z_iso_disp_transportf_fun_eq. exact Hff. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core.