intros S1 S2 H.
unfold lin_indep in |- *.
unfold not in |- *.
intros.
apply H0.
apply (lin_dep_include H).
assumption.
Qed.

(** For this we need $\neg\neg P\to P$: *)
Lemma lin_indep_prop :
forall (n : Nat) (a : seq n F) (v : seq n V),
distinct v ->
lin_indep (seq_set v) ->
sum (mult_by_scalars a v) =' (zero V) in _ -> a =' const_seq n (zero F) in _.