unfold lin_indep' in |- *.
unfold lin_dep in |- *.
split.
unfold not in |- *.
intros.
apply H.
exists n.
exists a.
exists v.
split.
assumption.
split.
assumption.
assumption.
unfold not in |- *.
intros.
inversion_clear H0.
inversion_clear H1.
inversion_clear H0.
apply (H x x0 x1).
inversion_clear H1.
assumption.
inversion_clear H1.
inversion_clear H2.
assumption.
inversion_clear H1.
inversion_clear H2.
assumption.
Qed.
End defs.
Section unexpected_true_results.

Lemma zero_imp_lin_dep :
forall (F : field) (V : vectorspace F) (X : part_set V),
in_part (zero V) X -> lin_dep X.