proposition: Proposition sym_mon_tensor_rassociator (x y z : V) : sym_mon_braiding (x ⊗ y) z = mon_lassociator x y z · identity x #⊗ sym_mon_braiding y z · mon_rassociator x z y · sym_mon_braiding x z #⊗ identity y · mon_lassociator z x y.
proof: Proof. refine (!_). rewrite !assoc'. etrans. { apply maponpaths. rewrite !assoc. rewrite <- sym_mon_hexagon_rassociator. rewrite !assoc'. rewrite mon_rassociator_lassociator. rewrite id_right. apply idpath. } rewrite !assoc. rewrite mon_lassociator_rassociator. apply id_left. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories