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_deloc :
forall (X : Typ1) (A : Rel X) (a : X),
deloc X A (opt X) (UNION X A a) (some X).