split; (elim X2; intros; elim X3; intros).
elim (a x); intros.
elim (a0 x0); intros.
exists x1.
apply X with (e0 x0); auto with zfc.
elim (b0 y); intros.
elim (b x); intros.
exists x0.
apply X with (e0 x); auto with zfc.
Qed.

Theorem EQC_sym : forall E1 E2 : Ens, EQC E1 E2 -> EQC E2 E1.
simple induction E1; simple induction E2; simpl in |- *; intros.