intros.
red in |- *.
exists n.
exists v.
auto with algebra.
Qed.
(** - This one is surprisingly hard to prove (or did I not think hard enough?) *)

Lemma included_reflects_is_finite_subset :
forall (A : Setoid) (B C : part_set A),
is_finite_subset C -> included B C -> is_finite_subset B.