Proposition sym_mon_hexagon_lassociator (x y z : V) : mon_lassociator x y z · sym_mon_braiding x (y ⊗ z) · mon_lassociator y z x = sym_mon_braiding x y #⊗ identity z · mon_lassociator y x z · identity y #⊗ sym_mon_braiding x z. Proof. pose (pr12 (pr222 V) x y z) as p. refine (p @ _). rewrite !assoc'. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. rewrite !assoc'. apply maponpaths. rewrite !assoc. apply maponpaths_2. 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.