Definition disp_vassocr' {a b : C} {f g h k : C⟦a,b⟧} {η : f ==> g} {φ : g ==> h} {ψ : h ==> k} {x : D a} {y : D b} {ff : x -->[f] y} {gg : x -->[g] y} {hh : x -->[h] y} {kk : x -->[k] y} (ηη : ff ==>[η] gg) (φφ : gg ==>[φ] hh) (ψψ : hh ==>[ψ] kk) : transportf (λ α, _ ==>[α] _) (vassocr _ _ _) (ηη •• (φφ •• ψψ)) = ((ηη •• φφ) •• ψψ). Proof. use (transportf_transpose_left (P := λ x' : f ==> k, ff ==>[x'] kk)). apply disp_vassocr. Defined.
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.