Lemma cancel_postcomposition_disp {C} {D : disp_cat C} {x y z} {f f' : x --> y} {e : f' = f} {g : y --> z} {xx : D x} {yy} {zz} {ff : xx -->[f] yy} {ff' : xx -->[f'] yy} (gg : yy -->[g] zz) (ee : ff = transportf _ e ff') : ff ;; gg = transportf _ (cancel_postcomposition _ _ g e) (ff' ;; gg). Proof. etrans. apply maponpaths_2, ee. apply mor_disp_transportf_postwhisker. Qed.
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.