intros A B.
case A; case B; simpl in |- *.
intros a pa b pb.
unfold eq_part in |- *; simpl in |- *.
intuition.
Qed.

(* Specifications: *)
Lemma diff_in_l :
forall (A B : part_set E) (x : E), in_part x (diff A B) -> in_part x A.
Lemma diff_in_r :
forall (A B : part_set E) (x : E), in_part x (diff A B) -> ~ in_part x B.
Lemma in_diff :
forall (A B : part_set E) (x : E),
in_part x A -> ~ in_part x B -> in_part x (diff A B).