proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Unitors