simple induction n.
simpl in |- *.
simple induction 1.
simple induction x.
intros.
change (IN E (Class_succ (Nat n0))) in H0.
elim (IN_Class_succ_or (Nat n0) E H0).
intros; exists n0.
auto with zfc.
intros.
elim (H E); auto with zfc.
Qed.

Theorem Omega_EQ_Union : EQ Omega (Union Omega).
apply INC_EQ; unfold INC in |- *.