Proposition mon_lassociator_lassociator {w x y z : V} : mon_lassociator (w ⊗ x) y z · mon_lassociator w x (y ⊗ z) = mon_lassociator w x y #⊗ identity z · mon_lassociator w (x ⊗ y) z · identity w #⊗ mon_lassociator x y z. Proof. refine (!(monoidal_pentagonidentity V w x y z) @ _). unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. rewrite (bifunctor_rightid V). rewrite (bifunctor_leftid V). rewrite !id_left, id_right. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.opp_precat. Import BifunctorNotations. Import MonoidalNotations. Section EquivalenceFromTensorWithUnit. Import MonoidalNotations. End EquivalenceFromTensorWithUnit. Import MonoidalNotations. Import MonoidalNotations. Import MonoidalNotations. Import MonoidalNotations. Import MonoidalNotations.