Lemma actegory_binprod_laws : actegory_laws Mon_V actegory_binprod_data. Proof. split. + exact actegory_binprod_action_data_is_bifunctor. + red; repeat split; try red; intros. - apply dirprodeq; apply actegory_unitornat. - apply dirprodeq; apply actegory_unitorisolaw. - apply dirprodeq; apply actegory_unitorisolaw. - apply dirprodeq; apply actegory_actornatleft. - apply dirprodeq; apply actegory_actornatright. - apply dirprodeq; apply actegory_actornatleftright. - apply dirprodeq; apply actegory_actorisolaw. - apply dirprodeq; apply actegory_actorisolaw. - apply dirprodeq; apply actegory_triangleidentity. - apply dirprodeq; apply actegory_pentagonidentity. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.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.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.ProductCategory. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.