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

Lemma UNION_eqv :
forall (X : Typ1) (A : Rel X) (a x : X),
EQV X A x (opt X) (UNION X A a) (some X x).