Definition actegory_binprod_action_data : bifunctor_data V CD CD. Proof. use make_bifunctor_data. * intros v cd. exact (v ⊗_{ActC} (pr1 cd),, v ⊗_{ActD} (pr2 cd)). * intros v cd1 cd2 fg. exact (v ⊗^{ActC}_{l} (pr1 fg),, v ⊗^{ActD}_{l} (pr2 fg)). * intros cd v1 v2 h. exact (h ⊗^{ActC}_{r} (pr1 cd),, h ⊗^{ActD}_{r} (pr2 cd)). Defined.
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.