Proposition sym_mon_hexagon_rassociator (x y z : V) : mon_rassociator x y z · sym_mon_braiding (x ⊗ y) z · mon_rassociator z x y = identity x #⊗ sym_mon_braiding y z · mon_rassociator x z y · sym_mon_braiding x z #⊗ identity y. Proof. pose (pr22 (pr222 V) x y z) as p. refine (p @ _). rewrite !assoc'. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. rewrite (bifunctor_leftid V). rewrite (bifunctor_rightid V). rewrite id_left, 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.