Proposition sym_mon_braiding_linvunitor (x : V) : mon_linvunitor x · sym_mon_braiding (I_{V}) x = mon_rinvunitor x. Proof. refine (!(id_right _) @ _ @ id_left _). rewrite <- mon_runitor_rinvunitor. rewrite !assoc. apply maponpaths_2. rewrite !assoc'. rewrite sym_mon_braiding_runitor. apply mon_linvunitor_lunitor. 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.