Lemma inverse_pentagon_4 {V W X Y Z : C} (k : C⟦Y,Z⟧) (h : C⟦X,Y⟧) (g : C⟦W,X⟧) (f : C⟦V,W⟧) : (lassociator g h k ⋆⋆ id₂ f) o rassociator f g (k ∘ h) = rassociator f (h ∘ g) k o id₂ k ⋆⋆ rassociator f g h o lassociator (g ∘ f) h k. Proof. rewrite <- !inverse_of_assoc. use vcomp_move_R_pM. { is_iso. } rewrite !vassocr. use vcomp_move_L_Mp. { is_iso. } use vcomp_move_L_Mp. { is_iso. } rewrite <- !vassocr. symmetry ; apply pentagon. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors.