simple induction E; unfold Union in |- *; simpl in |- *; intros A f r.
simple induction 1.
simple induction x.
intros a b; simpl in |- *.
intros.
exists (f a).
split.
exists a; auto with zfc.
apply CIN_sound_left with (pi2 (f a) b); auto with zfc.
simpl in |- *.
generalize b; elim (f a); simpl in |- *.
intros.
exists b0; auto with zfc.
Qed.

(* Specifications: *)
Theorem Union_soundC :
forall E E' : Ens, EQC E E' -> EQC (Union E) (Union E').
Theorem Union_soundC :
forall E E' : Ens, EQC E E' -> EQC (Union E) (Union E').