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