Proof
fun X A a x x' H E H1 _ _ =>
H1 x x' (eq_refl (opt X) (some X x)) (eq_refl (opt X) (some X x')) H.

(* Specifications: *)
Lemma SUCC_rt1 :
forall (X : Typ1) (A : Rel X) (a x' : X),
A x' a -> SUCC X A a (some X x') (none X).