Lemma is_z_iso_disp_independent_of_is_z_iso {C : category} {D : disp_cat_data C} {x y : C} (f : z_iso x y) {xx : D x} {yy} (ff : xx -->[f] yy) {H'f : is_z_isomorphism f} (Hff : is_z_iso_disp ((f : _ --> _),,H'f) ff) : is_z_iso_disp f ff. Proof. destruct f as [F Hf]. assert (E : Hf = H'f). apply isaprop_is_z_isomorphism. destruct E. exact Hff. Qed.
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.