Definition disp_vcomp_whisker {a b c : C} {f g : C⟦a,b⟧} {h i : C⟦b,c⟧} (η : f ==> g) (φ : h ==> i) (x : D a) (y : D b) (z : D c) (ff : x -->[f] y) (gg : x -->[g] y) (hh : y -->[h] z) (ii : y -->[i] z) (ηη : ff ==>[η] gg) (φφ : hh ==>[φ] ii) : (ηη ▹▹ hh) •• (gg ◃◃ φφ) = transportb (λ α, _ ==>[α] _) (vcomp_whisker _ _) ((ff ◃◃ φφ) •• (ηη ▹▹ ii)) := pr1 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 (pr2 D))))))))))))) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ηη φφ.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.