intros.
case (rep_ext n H).
intros; destruct s.
auto.
Qed.

Lemma grow_nr_elts :
forall (n k : Nat) (v : seq k V) (H : lin_indep (seq_set v) /\ distinct v),
has_n_elements k (seq_set v) ->
match rep_ext n H with
| existT i (existT w H') => has_n_elements i (seq_set w)
end.