intros.
elim (basis_iff_max_lin_indep beta).
intros.
apply H; auto with algebra.
exact (is_basis_prf beta).
Qed.

(** - %\intoc{\bf Theorem 1.13}%: *)
Lemma max_lin_indep_subset_generated :
forall (F : field) (V : vectorspace F) (W : part_set V),
lin_indep W ->
exists W' : part_set V, max_lin_indep W' (full V) /\ included W W'.