intros; red in |- *; red in H.
inversion_clear H; inversion_clear H0.
exists x; exists (Map_embed x0).
destruct x0; simpl in H; red in H; simpl in H; simpl in |- *; red in |- *;
simpl in |- *.
split; intros.
red in H0; elim (H (Build_subtype H0)).
intros p _; generalize (p I); clear p; intro.
inversion_clear H1.
red in H2.
exists x1.
simpl in H2.
auto.
inversion_clear H0.
apply in_part_comp_l with (subtype_elt (Ap x1)); auto with algebra.
Qed.

(* Specifications: *)
Lemma seq_set_is_finite_subset :
forall (A : Setoid) (n : Nat) (v : seq n A), is_finite_subset (seq_set v).