Lemma triangle_r {X Y Z : C} (g : C⟦Y,Z⟧) (f : C⟦X,Y⟧) : lunitor g ⋆⋆ id₂ f = (id₂ g ⋆⋆ runitor f) o lassociator f (id₁ Y) g. Proof. cbn. apply pathsinv0. unfold hcomp. etrans. { apply maponpaths. etrans. { apply maponpaths. apply lwhisker_id2. } apply id2_right. } etrans. { apply runitor_rwhisker. } apply pathsinv0. etrans. { apply maponpaths_2. apply id2_rwhisker. } 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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors.