proposition: Lemma lax_lineator_postcomp_SelfActCAT_laws : lineator_laxlaws (Mon_endo C) (SelfActCAT C) (SelfActCAT C) (post_comp_functor G) lax_lineator_postcomp_SelfActCAT_data.
proof: Proof. split4. - intro; intros. apply (nat_trans_eq C). intro c. cbn. rewrite id_left; apply id_right. - intro; intros. apply (nat_trans_eq C). intro c. cbn. rewrite id_left; apply id_right. - intro; intros. apply (nat_trans_eq C). intro c. cbn. do 3 rewrite id_left. apply functor_id. - intro; intros. apply (nat_trans_eq C). intro c. cbn. rewrite id_left. apply functor_id. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.BicatOfCatsElementary UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Actegories.Examples.ActionOfEndomorphismsInCATElementary UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Actegories.CoproductsInActegories