Lemma remove_ε₁ : ε₁ o runitor (l ∘ r₁) o lassociator r₁ l (id₁ Y) o (ε₂ ▻ l o rassociator l r₂ l o l ◅ η₂ o linvunitor l) ▻ r₁ = ε₁. Proof. rewrite !vassocr. rewrite !(maponpaths (λ z, z • _) (!(vassocr _ _ _))). rewrite <- runitor_triangle. rewrite !vassocr. refine (_ @ id2_left _). apply (maponpaths (λ z, z • _)). rewrite <- !vassocr. rewrite <- lwhisker_id2. rewrite <- (internal_triangle1 A₂). rewrite <- !lwhisker_vcomp. rewrite <- !vassocr. repeat (apply maponpaths). rewrite !vassocr. rewrite lassociator_rassociator. 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.