Lemma runitor_lunitor_identity (a : C) : runitor (identity a) = lunitor (identity a). Proof. apply (vcomp_lcancel (lunitor _ )). { apply is_invertible_2cell_lunitor. } etrans. { apply pathsinv0. apply vcomp_lunitor. } etrans. { apply maponpaths_2. apply lwhisker_runitor_lunitor. } apply maponpaths_2. apply (!lunitor_is_lunitor_lwhisker _). 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.Examples.OpMorBicat. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat.