Proof
fun X A a x x' H E e _ _ =>
e x x' (eq_refl (sum X (X -> Prop)) (inl X (X -> Prop) x'))
(eq_refl (sum X (X -> Prop)) (inl X (X -> Prop) x)) H.

Lemma POWER_in2 :
forall (X : Typ1) (A : Rel X) (a x' : X) (p : X -> Prop),
A x' a -> p x' -> POWER X A a (inl X (X -> Prop) x') (inr X (X -> Prop) p).