Proposition sym_mon_braiding_runitor (x : V) : sym_mon_braiding (I_{V}) x · mon_runitor x = mon_lunitor x. Proof. rewrite <- sym_mon_braiding_lunitor. rewrite !assoc. rewrite sym_mon_braiding_inv. apply id_left. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Import MonoidalNotations.