Proposition sym_mon_hexagon_rassociator1 (x y z : V) : sym_mon_braiding (x ⊗ y) z · mon_rassociator z x y · sym_mon_braiding z x ⊗^{ V}_{r} y = mon_lassociator x y z · x ⊗^{ V}_{l} sym_mon_braiding y z · mon_rassociator x z y. Proof. etrans. 2: { apply maponpaths_2. apply sym_mon_hexagon_rassociator0. } etrans. 2: { rewrite assoc'. apply maponpaths. apply pathsinv0, mon_lassociator_rassociator. } rewrite ! assoc'. 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.