Goal:
  
  A : Type
  a : option A
  l : list (option A)
  f : A -> A
  IHl : map_option_out (map (option_map f) l) =
        option_map (map f) (map_option_out l)
  fa : option_map f a = None
  ============================
   (None =
    option_map (map f)
      match a with
      | Some hd =>
          match map_option_out l with
          | Some tl => Some (hd :: tl)
          | None => None
          end
      | None => None
      end)


DEBUG:Going to execute:
destruct a; simpl in *