Proof
fun X A a P x x' H E e _ =>
e x x' (eq_refl (opt X) (some X x)) (eq_refl (opt X) (some X x')) H.

Lemma SELECT_rt :
forall (X : Typ1) (A : Rel X) (a : X) (P : PRED) (x' : X),
A x' a -> P X A x' -> SELECT X A a P (some X x') (none X).