Proposition sym_mon_hexagon_rassociator0 (x y z : V) : sym_mon_braiding (x ⊗ y) z · mon_rassociator z x y · sym_mon_braiding _ _ ⊗^{V}_{r} y · mon_lassociator _ _ _ = mon_lassociator x y z · x ⊗^{V}_{l} sym_mon_braiding y z. Proof. rewrite sym_mon_tensor_rassociator. rewrite ! assoc'. etrans. { do 4 apply maponpaths. rewrite assoc. now rewrite mon_lassociator_rassociator. } rewrite id_left. apply maponpaths. etrans. { do 2 apply maponpaths. rewrite assoc. do 2 apply maponpaths_2. apply (when_bifunctor_becomes_rightwhiskering V). } etrans. { do 2 apply maponpaths. apply maponpaths_2. apply pathsinv0, (bifunctor_rightcomp V). } rewrite sym_mon_braiding_inv. rewrite (bifunctor_rightid V). rewrite id_left. rewrite mon_rassociator_lassociator. rewrite id_right. apply (when_bifunctor_becomes_leftwhiskering V). 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.