proposition: Lemma disp_vassocl {D : disp_prebicat} {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) : (ηη •• φφ) •• ψψ = transportb (λ α, _ ==>[α] _) (vassocl _ _ _) (ηη •• (φφ •• ψψ)).
proof: Proof. apply (transportf_transpose_right (P := λ x', _ ==>[x'] _)). apply pathsinv0. etrans. { apply disp_vassocr. } apply maponpaths_2. unfold vassocl. apply pathsinv0, pathsinv0inv0. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Univalence