elim H0; simple induction x; intros; exists x0; auto with zfc.
Qed.

(* Specifications: *)
Theorem IN_Comp_P :
forall (E A : Ens) (P : Ens -> Prop),
(forall w1 w2 : Ens, P w1 -> EQ w1 w2 -> P w2) -> IN A (Comp E P) -> P A.
Theorem IN_Comp_P :
forall (E A : Ens) (P : Ens -> Prop),
(forall w1 w2 : Ens, P w1 -> EQ w1 w2 -> P w2) -> IN A (Comp E P) -> P A.