Definition compact_sum_map {X: Type} {F F0: X -> Type} (l: list X)
  (f: ListType (map (fun x => F x -> F0 x) l)): compact_sum (map F l) -> compact_sum (map F0 l).

Lemma compact_sum_map_single: forall {X: Type} {F F0: X -> Type} (x: X) (f: F x -> F0 x) (v: F x), compact_sum_map (x :: nil) (Cons f Nil) v = f v.