Lemma mor_disp_transportf_prewhisker {C : precategory} {D : disp_cat_data C} {x y z : C} {f : x --> y} {g g' : y --> z} (eg : g = g') {xx : D x} {yy} {zz} (ff : xx -->[f] yy) (gg : yy -->[g] zz) : ff ;; (transportf _ eg gg) = transportf _ (maponpaths (compose f) eg) (ff ;; gg). Proof. destruct eg; 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.