Proposition sym_mon_braiding_id : sym_mon_braiding I_{V} I_{V} = identity (I_{V} ⊗ I_{V}). Proof. refine (_ @ mon_runitor_rinvunitor _). rewrite <- sym_mon_braiding_lunitor. rewrite !assoc'. rewrite mon_lunitor_I_mon_runitor_I. rewrite mon_runitor_rinvunitor. rewrite id_right. apply idpath. 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.