Lemma monoidal_leftunitorinvnat {C : category} (M : monoidal C) : leftunitorinv_nat luinv_{M}. Proof. intros x y f. apply (z_iso_inv_on_right _ _ _ (_,,_,,monoidal_leftunitorisolaw M x)). cbn. rewrite assoc. apply (z_iso_inv_on_left _ _ _ _ (_,,_,,monoidal_leftunitorisolaw M y)). apply pathsinv0, monoidal_leftunitornat. 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.