Section MAIN.
Variable F : field.
Variable V : vectorspace F.
Variable W0 : part_set V.
Variable H : is_finite_subset W0.
Variable H0 : generates W0 (full V).

(** - %\intoc{\bf Theorem 1.9}% in various flavours: *)
Lemma every_finite_generating_set_has_a_subset_that_is_a_basis :
exists W : part_set W0, is_basis (inject_subsets W).