proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.TransportLaws UniMath.Bicategories.Core.EquivToAdjequiv