intros.
generalize (n_element_subset_sequence H).
intros (v, (E, D)).
apply Trans with (seq_set v); auto with algebra.
Qed.

(* Specifications: *)
Lemma empty_then_has_zero_elements :
forall (A : Setoid) (B : part_set A),
B =' empty A in _ -> has_n_elements 0 B.