Lemma monoidal_associatorinv_nat2 {C : category} (M : monoidal C) {x x' y y' z z' : C} (f : C⟦x,x'⟧) (g : C⟦y,y'⟧) (h : C⟦z,z'⟧) : (f ⊗^{M} (g ⊗^{M} h)) · (αinv_{M} x' y' z') = (αinv_{M} x y z) · ((f ⊗^{M} g) ⊗^{M} h). Proof. intros. unfold functoronmorphisms1. apply monoidal_associatorinv_nat1. 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.