Proof
fun X A a P x' H1 H2 E _ e =>
e x' (eq_refl (opt X) (some X x')) (eq_refl (opt X) (none X)) H1 H2.

Lemma SELECT_eqv :
forall (X : Typ1) (A : Rel X) (a : X) (P : PRED) (x : X),
EQV X A x (opt X) (SELECT X A a P) (some X x).