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