intros.
exists (cast_map_to_subset H).
auto with algebra.
Qed.
Hint Resolve seq_castable: algebra.

Lemma subset_seq_castable :
forall (A D : Setoid) (B C : part_set A) (v : MAP D B)
(H : forall i : D, in_part (Map_embed v i) C),
exists w : MAP D C, Map_embed w =' Map_embed v in _.