Definition ComposeApplicative : Applicative.
exists FG Compose_pure Compose_ap.
apply Compose_identity.
apply Compose_composition.
apply Compose_homomorphism.
apply Compose_interchange.
Defined.
End ComposeApplicative.

Lemma sequenceVector_map n a b (F:Applicative) (f : a -> b) (v :Vector.t (F a) n) :
map (Vector.map f) (sequenceVector v) = sequenceVector (Vector.map (map f) v).