Proposition sym_mon_braiding_rinvunitor (x : V) : mon_rinvunitor x · sym_mon_braiding x (I_{V}) = mon_linvunitor x. Proof. refine (!(id_right _) @ _ @ id_left _). rewrite <- mon_lunitor_linvunitor. rewrite !assoc. apply maponpaths_2. rewrite !assoc'. rewrite sym_mon_braiding_lunitor. apply mon_rinvunitor_runitor. 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.