Section MAIN.
Variable F : field.
Variable V : vectorspace F.

(** - %\intoc{Corollary 1 to 1.10}% *)
Lemma finite_bases_always_equally_big :
forall (n : Nat) (beta : basis V),
has_n_elements n beta ->
forall Sset : part_set V,
lin_indep Sset -> has_n_elements n Sset -> is_basis Sset.