header {* Distributive law for the sum of 2 *} (* This is similar to Distributive_Law, but assumes a distributive law Λ1 over (SpK,ΣΣ1,F) instead of (S,ΣΣ1,F): *) theory Tree_Distributive_Law1 imports Tree_Integrate_New_Op1 begin (* We assume (S,ΣΣ,F)-distributive law, where: -- S is the syntactic signature and T is its term extension (free algebra extension) -- F is the behavior functor *) (* (* Distributive law: *) consts Λ1 :: "('a × 'a F) SpK => 'a ΣΣ1 F" axiomatization where Λ1_natural: "Λ1 o SpKmap (f ** Fmap f) = Fmap (T1_map f) o Λ1" *) end