Definition assoc_disp_var {C} {D : disp_cat C} {x y z w} {f} {g} {h} {xx : D x} {yy : D y} {zz : D z} {ww : D w} (ff : xx -->[f] yy) (gg : yy -->[g] zz) (hh : zz -->[h] ww) : (ff ;; gg) ;; hh = transportf _ (assoc _ _ _) (ff ;; (gg ;; hh)). Proof. apply pathsinv0, transportf_pathsinv0. apply pathsinv0, assoc_disp. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.AxiomOfChoice. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering.