Section unexpected_true_results.
intros.
unfold lin_dep in |- *.
exists 0.
exists (const_seq 1 (ring_unit F)).
red in H.
exists (const_seq 1 (Build_subtype H:X)).
split.
red in |- *.
intros i j.
generalize fin_S_O_unique.
intros.
absurd (i =' j in _); auto.
split.
cut (~ one =' (zero F) in _).
unfold not in |- *.
intros.
apply H0.
simpl in H1.
red in H1.
simpl in H1.
apply H1.
exact (Build_finiteT (lt_O_Sn 0)).
exact (field_unit_non_zero F).
simpl in |- *.
apply Trans with ((zero V) +' (zero V)); auto with algebra.
Qed.

Lemma empty_lin_indep :
forall (F : field) (V : vectorspace F), lin_indep (empty V).