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_Id  n a (v: Vector.t a n) :
sequenceVector (F:=IdApplicative) v = v.