intros.
auto with algebra.
Qed.
Hint Resolve Map_embed_eats_cast_map_to_subset: algebra.

Lemma seq_castable :
forall (A B : Setoid) (v : MAP B A) (W : part_set A),
(forall i : B, in_part (v i) W) -> exists w : MAP B W, Map_embed w =' v in _.