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

(* Specifications: *)
Lemma UNION_rt :
forall (X : Typ1) (A : Rel X) (a x x' : X),
A x' x -> A x a -> UNION X A a (some X x') (none X).