Definition KSApplicative (i j : Type) : Applicative.Definition Compose_pure (a:Type) (x:a) : FG a :=
  pure F (pure G x).Definition Compose_ap (a b:Type) (f:FG (a -> b)) (x:FG a) : FG b :=
 ap (ap (pure F (fun g x => ap g x)) f) x.

Lemma Compose_homomorphism a b (f : a -> b) x : Compose_ap (Compose_pure f) (Compose_pure x) = Compose_pure (f x).