Definition fin_stream {A: Type} (h: list A) : stream A.
exists (fun n => nth_error h n).
intros.
rewrite nth_error_None_iff in H0 |- *.
omega.
Defined.
Definition inf_stream {A: Type} (h: nat -> A) : stream A.
exists (fun n => Some (h n)).
intros.
congruence.
Defined.

Lemma inf_stream_inf {A: Type}: forall f: nat -> A, is_inf_stream (inf_stream f).