Lemma mor_disp_transportf_postwhisker {C : precategory} {D : disp_cat_data C} {x y z : C} {f f' : x --> y} (ef : f = f') {g : y --> z} {xx : D x} {yy} {zz} (ff : xx -->[f] yy) (gg : yy -->[g] zz) : (transportf _ ef ff) ;; gg = transportf _ (cancel_postcomposition _ _ g ef) (ff ;; gg). Proof. destruct ef; apply idpath. 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.