Lemma inverse_pentagon_2 {V W X Y Z : C} (k : C⟦Y,Z⟧) (h : C⟦X,Y⟧) (g : C⟦W,X⟧) (f : C⟦V,W⟧) : rassociator (g ∘ f) h k o (lassociator f g h ⋆ id2 k) = lassociator f g (k ∘ h) o (f ◃ rassociator g h k) o rassociator f (h ∘ g) k. Proof. rewrite <- !inverse_of_assoc. use vcomp_move_R_Mp. { is_iso. } rewrite <- vassocr. use vcomp_move_L_pM. { is_iso. } rewrite <- vassocr. use vcomp_move_L_pM. { is_iso. } symmetry. pose (pentagon k h g f) as p. unfold hcomp in p. rewrite id2_rwhisker in p. rewrite id2_left in p. exact p. 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.