proposition: Lemma actegory_binprod_laws : actegory_laws Mon_V actegory_binprod_data.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.ProductCategory