intros.
unfold empty in |- *.
red in |- *.
red in |- *.
unfold lin_dep in |- *.
intro.
inversion_clear H.
inversion_clear H0.
inversion_clear H.
set (h := head x1) in *.
case h.
simpl in |- *.
auto.
Qed.
End unexpected_true_results.
Section more.
Variable F : field.
Variable V : vectorspace F.

(** - %\intoc{\bf Theorem 1.6}% *)
Lemma lin_dep_include :
forall S1 S2 : part_set V, included S1 S2 -> lin_dep S1 -> lin_dep S2.