Lemma remove_η₂ : r₂ ◅ (runitor l o ε₁ ▻ l o rassociator l r₁ l o l ◅ η₁) o lassociator (id₁ X) l r₂ o linvunitor (r₂ ∘ l) o η₂ = η₂. Proof. refine (_ @ id2_right _). apply maponpaths. rewrite <- hcomp_identity. rewrite <- (internal_triangle1 A₁). rewrite <- rwhisker_hcomp. rewrite <- !rwhisker_vcomp. rewrite linvunitor_assoc. rewrite <- !vassocr. apply maponpaths. rewrite !vassocr. rewrite rassociator_lassociator. apply (maponpaths (fun z => ((z • _) • _) • _)). apply 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.