Definition disp_functor_comp_var {C' C} {F} {D' : disp_cat C'} {D : disp_cat C} (FF : disp_functor F D' D) {x y z} {xx : D' x} {yy} {zz} {f : x --> y} {g : y --> z} (ff : xx -->[f] yy) (gg : yy -->[g] zz) : transportf _ (functor_comp F f g) (♯ FF (ff ;; gg)) = ♯ FF ff ;; ♯ FF gg. Proof. apply transportf_pathsinv0. apply pathsinv0, disp_functor_comp. Defined.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.