Lemma left_unit_assoc {X Y Z : C} (g : C⟦Y,Z⟧) (f : C⟦X,Y⟧) : (runitor g) ▻ f = runitor (g ∘ f) o lassociator f g (id₁ Z). Proof. rewrite <- runitor_triangle. unfold assoc. rewrite vassocr. rewrite lassociator_rassociator. rewrite id2_left. apply idpath. 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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors.