Definition disp_z_iso_inv_on_left {C : category} {D : disp_cat C} {x y z : C} {f : x --> y} {g : y --> z} {h : x --> z} (Hf : is_z_isomorphism f) {xx : D x} {yy : D y} {zz : D z} {ff : xx -->[ f ] yy} {gg : yy -->[ g ] zz} {hh : xx -->[ h ] zz} (Hff : is_z_iso_disp (f ,, Hf) ff) (p : f · g = h) : gg = transportf _ (z_iso_inv_on_right _ _ _ (f,,Hf) g h (! p)) (pr1 Hff ;; hh) -> ff ;; gg = transportb _ p hh.
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.