proposition: Proposition sym_mon_tensor_lassociator (x y z : V) : sym_mon_braiding x (y ⊗ z) = mon_rassociator x y z · sym_mon_braiding x y #⊗ identity z · mon_lassociator y x z · identity y #⊗ sym_mon_braiding x z · mon_rassociator y z x.
proof: Proof. refine (!_). rewrite !assoc'. etrans. { apply maponpaths. rewrite !assoc. rewrite <- sym_mon_hexagon_lassociator. rewrite !assoc'. rewrite mon_lassociator_rassociator. rewrite id_right. apply idpath. } rewrite !assoc. rewrite mon_rassociator_lassociator. 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