intros.
red in H.
apply is_subspace_comp with (span S:part_set V); auto.
apply is_subspace_OK.
Qed.

(* Specifications: *)
Lemma is_lin_comb_from_generates :
forall (F : field) (V : vectorspace F) (S W : part_set V),
generates S W -> forall x : V, in_part x W -> is_lin_comb x S.