intros.
red in H.
inversion_clear H.
inversion_clear H0.
exists (Map_embed x).
simpl in H.
red in H.
simpl in H.
split; simpl in |- *.
red in |- *.
simpl in |- *.
intro a; split; intros.
generalize (H (Build_subtype H0)); clear H; intros (p, q); generalize (p I);
clear p q; intro.
inversion_clear H.
red in H2.
exists x0.
simpl in H2.
auto.
inversion_clear H0.
apply in_part_comp_l with (subtype_elt (x x0)); auto with algebra.
apply Map_embed_preserves_distinct; auto with algebra.
Qed.

Lemma seq_set_n_element_subset :
forall (A : Setoid) (n : Nat) (B : part_set A),
(exists v : seq n A, B =' seq_set v in _ /\ distinct v) ->
has_n_elements n B.