Section MAIN.
Variable F : field.
Variable V : findimvecsp F.
Variable W : subspace V.
Let H : lin_indep (seq_set (empty_seq W)) /\ distinct (empty_seq W).
split; try apply lin_indep_comp with (empty W); auto with algebra.
apply empty_lin_indep.
intro.
auto with algebra.
Qed.

Lemma grow_bound :
forall n : nat,
match rep_ext n H with
| existT i (existT w H') => i <= n
end.