Lemma pentagon {C : bicat} {V W X Y Z : C} (k : C⟦Y,Z⟧) (h : C⟦X,Y⟧) (g : C⟦W,X⟧) (f : C⟦V,W⟧) : (lassociator (g ∘ f) h k o lassociator f g (k ∘ h)) = (id₂ k ⋆⋆ lassociator f g h) o lassociator f (h ∘ g) k o (lassociator g h k ⋆⋆ id₂ f). Proof. unfold assoc. unfold hcomp. apply pathsinv0. rewrite id2_rwhisker. rewrite id2_left. rewrite lwhisker_id2. rewrite id2_right. rewrite vassocr. apply lassociator_lassociator. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations.