Program Definition stream_capp {A: Type} (h: nat -> stream A): stream A :=
  fun n: nat =>
    match partial_stream_clen' h n return option A with
    | Some (k, m) => h k m
    | None => None
    end.

Lemma stream_capp_empty0 {A: Type}: forall (h: nat -> stream A), is_empty_stream (h 0) -> is_empty_stream (stream_capp h).