intros.
red in |- *.
exists (Build_basis H).
simpl in |- *.
auto.
Qed.
Section Part_3.

(** - %\intoc{Corollary 4 to 1.10}% *)
Lemma dimension_bounds_generating_set_size :
forall (F : field) (V : vectorspace F) (n : Nat),
has_dim n V ->
forall S : part_set V,
generates S (full V) ->
has_at_most_n_elements n S -> is_basis S /\ has_n_elements n S.