Program Definition stream_app {A: Type} (h1 h2: stream A): stream A :=
  fun n: nat =>
    match partial_stream_len h1 n return option A with
    | None => h1 n
    | Some m => h2 (n - m)
    end.

Lemma stream_app_empty_stream {A: Type}: forall (h: stream A), stream_app h empty_stream = h.