intros.
generalize (finite_basis_bounds_lin_indep_set_size H).
intro p; generalize (p Sset); clear p; intro p.
apply not_at_least_then_at_most; auto with algebra.
Qed.
(** - %\intoc{Corollary 3 to 1.10}% *)

Lemma all_finite_bases_equally_big :
forall (n : Nat) (beta : basis V),
has_n_elements n beta -> forall Sset : basis V, has_n_elements n Sset.