Lemma transportf_z_iso_disp {C : category} {D : disp_cat C} {x y : C} {xx : D x} {yy} {f f' : z_iso x y} (e : f = f') (ff : z_iso_disp f xx yy) : pr1 (transportf (λ g, z_iso_disp g _ _) e ff) = transportf _ (maponpaths pr1 e) (pr1 ff). Proof. destruct e; apply idpath. 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.