Program Definition fstn_stream {A: Type} (n: nat) (h: stream A) : stream A :=
fun m => if le_lt_dec n m then None else h m.
Next Obligation.
destruct (le_lt_dec n x), (le_lt_dec n y); try congruence.
+ omega.
+ apply (stream_sound1 h x y); auto; omega.
Qed.
Definition skipn_stream {A: Type} (n: nat) (h: stream A) : stream A.
exists (fun m => h (m + n)).
intros.
revert H0; apply (stream_sound1 h).
omega.
Defined.

Lemma skipn_stream_empty {A: Type}: forall n (h: stream A),
is_at_most_n_stream n h ->
skipn_stream n h = empty_stream.