proposition: Lemma actegory_binprod_pr1_lineator_lax_laws : lineator_laxlaws _ _ _ _ actegory_binprod_pr1_lineator_data.
proof: 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.
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