unfold inter in |- *; simpl in |- *.
unfold eq_part in |- *; simpl in |- *.
intros A A' B B' H' H'0 x.
generalize (H' x) (H'0 x); tauto.
Qed.

Lemma inter_assoc :
forall A B C : part_set E, Equal (inter A (inter B C)) (inter (inter A B) C).