simple induction E; simpl in |- *; intros B f Hr A P H i; elim i; intros c;
elim c; simpl in |- *; intros x q e; apply H with (f x);
auto with zfc.
Qed.

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