intros.
apply seq_set_n_element_subset; auto with algebra.
exists (empty_seq A).
split.
apply Trans with (empty A); auto with algebra.
red in |- *.
intros.
apply False_ind; auto with algebra.
Qed.
Hint Resolve has_zero_elements_then_empty empty_then_has_zero_elements:
algebra.

Lemma full_preserves_has_n_elements :
forall (A : Setoid) (n : Nat),
has_n_elements n A -> has_n_elements n (full A).