Lemma actegory_unitorinvnat {C : category} (Act : actegory C) : action_unitorinv_nat auinv_{Act}. Proof. intros x y f. apply (z_iso_inv_on_right _ _ _ (_,,_,,actegory_unitorisolaw Act x)). cbn. rewrite assoc. apply (z_iso_inv_on_left _ _ _ _ (_,,_,,actegory_unitorisolaw Act y)). apply pathsinv0, actegory_unitornat. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Foundations.All. 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.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Import MonoidalNotations. Section EquivalenceFromTensorWithUnit. Import MonoidalNotations. End EquivalenceFromTensorWithUnit. Import MonoidalNotations. Import ActegoryNotations.