red in |- *.
intros.
red in H0.
inversion H0.
inversion H1.
exists x.
exists x0.
apply Trans with B; auto with algebra.
Qed.
(** - There is no corresponding is_finite_set_comp, for there is no 'master' setoid wherein two Setoids can be compared. *)
Hint Resolve is_finite_subset_comp: algebra.

Lemma is_finite_subset_then_is_finite :
forall (A : Setoid) (B : part_set A), is_finite_subset B -> is_finite_set B.