Proposition sym_mon_tensor_rassociator (x y z : V) : sym_mon_braiding (x ⊗ y) z = mon_lassociator x y z · identity x #⊗ sym_mon_braiding y z · mon_rassociator x z y · sym_mon_braiding x z #⊗ identity y · mon_lassociator z x y. Proof. refine (!_). rewrite !assoc'. etrans. { apply maponpaths. rewrite !assoc. rewrite <- sym_mon_hexagon_rassociator. rewrite !assoc'. rewrite mon_rassociator_lassociator. rewrite id_right. apply idpath. } rewrite !assoc. rewrite mon_lassociator_rassociator. 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.