Proof
fun X A a x' p H1 H2 E _ e _ =>
e x' p (eq_refl (sum X (X -> Prop)) (inl X (X -> Prop) x'))
(eq_refl (sum X (X -> Prop)) (inr X (X -> Prop) p)) H1 H2.

Lemma POWER_rt :
forall (X : Typ1) (A : Rel X) (a : X) (p : X -> Prop),
POWER X A a (inr X (X -> Prop) p) (out X (X -> Prop)).