unfold included in |- *; simpl in |- *; intuition.
Qed.

(* Specifications: *)
Lemma union_comp :
forall A A' B B' : part_set E,
Equal A A' -> Equal B B' -> Equal (union A B) (union A' B').
Lemma inter_comp :
forall A A' B B' : part_set E,
Equal A A' -> Equal B B' -> Equal (inter A B) (inter A' B').