Lemma mor_disp_transportb_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 ;; (transportb _ eg gg') = transportb _ (maponpaths (compose f) (eg)) (ff ;; gg'). Proof. destruct eg; apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Core.Isos. Import BifunctorNotations. Import DisplayedBifunctorNotations.