red in |- *.
intros.
unfold uninject_subsetsify in |- *.
destruct x; destruct y.
simpl in |- *.
red in |- *.
simpl in |- *.
auto with algebra.
Qed.

Lemma in_part_included :
forall (A : Setoid) (B C : part_set A) (a : A),
in_part a B -> included B C -> in_part a C.