proposition: Lemma actegory_from_precomp_laws : actegory_laws Mon_endo actegory_from_precomp_data.
proof: Proof. split5. - exact action_from_precomp_laws. - split. + intros f g β. cbn. apply vcomp_lunitor. + split. * cbn. apply lunitor_linvunitor. * cbn. apply linvunitor_lunitor. - split4. + intros v w f f' β. cbn. apply lwhisker_lwhisker_rassociator. + intros v v' w f α. cbn. apply pathsinv0, rwhisker_rwhisker_alt. + intros v w w' f α. cbn. apply rwhisker_lwhisker_rassociator. + split. * cbn. apply rassociator_lassociator. * cbn. apply lassociator_rassociator. - intros v f. cbn. apply lunitor_lwhisker. - intros w v v' f. cbn. apply rassociator_rassociator. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.Bicategories.MonoidalCategories.WhiskeredMonoidalFromBicategory UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Actegories.Examples.ActionOfEndomorphismsInCATElementary UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Examples.BicatOfCats UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Actegories.CoproductsInActegories