simple induction E'; intros A' f' HR'; simpl in |- *; simple induction 1;
intros a' e'; exists (f' a'); auto with zfc.
Qed.

Theorem Big_closed_for_power : forall E : Ens, IN E Big -> IN (Power E) Big.
unfold Big in |- *; simpl in |- *; intros E; simple induction 1;
intros E' HE'; exists (Power' E').