Lemma actegory_binprod_pr1_lineator_lax_laws : lineator_laxlaws _ _ _ _ actegory_binprod_pr1_lineator_data. Proof. red; repeat split; red; intros. - rewrite id_left. apply id_right. - rewrite id_left. apply id_right. - cbn. unfold actegory_binprod_pr1_lineator_data. rewrite id_left, id_right. etrans. 2: { apply maponpaths. apply pathsinv0, (functor_id (leftwhiskering_functor ActC v)). } apply pathsinv0, id_right. - apply id_left. 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.