Proposition sym_mon_tensor_lassociator0 (x y z : V) : sym_mon_braiding x (y ⊗ z) · mon_lassociator y z x = mon_rassociator x y z · sym_mon_braiding x y #⊗ identity z · mon_lassociator y x z · identity y #⊗ sym_mon_braiding x z. Proof. rewrite sym_mon_tensor_lassociator. rewrite ! assoc'. rewrite mon_rassociator_lassociator. now rewrite id_right. 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.