Proposition mon_lassociator_lassociator' {w x y z : V} : mon_lassociator (w ⊗ x) y z · mon_lassociator w x (y ⊗ z) · w ⊗^{V}_{l} mon_rassociator x y z = mon_lassociator w x y ⊗^{V}_{r} z · mon_lassociator w (x ⊗ y) z. Proof. etrans. { apply maponpaths_2. apply mon_lassociator_lassociator. } rewrite <- (when_bifunctor_becomes_leftwhiskering V). rewrite ! assoc'. etrans. { do 2 apply maponpaths. apply pathsinv0, tensor_comp_id_l. } etrans. { do 2 apply maponpaths. apply maponpaths. apply mon_lassociator_rassociator. } rewrite tensor_id_id. rewrite id_right. apply maponpaths_2. apply (when_bifunctor_becomes_rightwhiskering V). 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.