Lemma actegory_binprod_delta_lineator_lax_laws : lineator_laxlaws _ _ _ _ actegory_binprod_delta_lineator_data. Proof. red; repeat split; red; intros. - cbn. apply maponpaths_12; (rewrite id_left; apply id_right). - cbn. apply maponpaths_12; (rewrite id_left; apply id_right). - cbn. apply maponpaths_12; unfold actegory_binprod_pr2_lineator_data; (rewrite id_left, id_right); (etrans; [| apply maponpaths; apply pathsinv0, (functor_id (leftwhiskering_functor Act v))]; apply pathsinv0, id_right). - cbn. apply maponpaths_12; 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.