Corollary unitorsinv_coincide_on_unit : luinv_{M} I_{M} = ruinv_{M} I_{M}. Proof. apply (cancel_z_iso _ _ (lu_{M} I_{M},,(luinv_{M} I_{M},,monoidal_leftunitorisolaw M I_{M}))). cbn. etrans. 2: { rewrite unitors_coincide_on_unit. apply pathsinv0, (monoidal_rightunitorisolaw M I_{M}). } apply (monoidal_leftunitorisolaw M I_{M}). 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.