Lemma help_triangle_ε : ε₂ o l ◅ (lunitor r₂ o r₂ ◅ ε₁) = ε₁ o runitor (l ∘ r₁) o lassociator _ _ _ o ε₂ ▻ l ▻ r₁ o rassociator _ _ _ o rassociator _ _ _. Proof. rewrite !vassocr. rewrite !(maponpaths (λ z, (z • _) • _) (!(vassocr _ _ _))). rewrite !lwhisker_hcomp, !rwhisker_hcomp. rewrite hcomp_lassoc. rewrite !vassocr. rewrite !(maponpaths (λ z, ((z • _) • _) • _) (!(vassocr _ _ _))). rewrite rassociator_lassociator, id2_right. rewrite <- !vassocr. use vcomp_move_L_pM. { is_iso. } cbn. rewrite <- runitor_natural. rewrite !vassocr. rewrite hcomp_identity. rewrite <- interchange. rewrite !id2_right, id2_left. rewrite <- !rwhisker_hcomp. rewrite <- rwhisker_vcomp. rewrite !vassocr. rewrite !rwhisker_hcomp. rewrite <- hcomp_lassoc. rewrite !(maponpaths (λ z, z • _) (!(vassocr _ _ _))). rewrite <- !rwhisker_hcomp. rewrite lunitor_triangle. rewrite <- !vassocr. rewrite <- vcomp_lunitor. rewrite lunitor_runitor_identity. rewrite !vassocr. apply (maponpaths (λ z, z • _)). rewrite lwhisker_hcomp, rwhisker_hcomp. rewrite hcomp_identity. rewrite <- interchange. rewrite !id2_right. apply (maponpaths (fun z => (z ⋆⋆ _))), id2_left. 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.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv.