Next Obligation.
pose proof proj2_sig h x y H.
change (proj1_sig h) with (stream_get h) in H1.
destruct (h x), (h y); try congruence.
specialize (H1 eq_refl); congruence.
Qed.

Lemma stream_map_spec {A B: Type}: forall (f: A -> B) (h: stream A) (n: nat),
stream_map f h n =
match h n return option B with
| Some a => Some (f a)
| None => None
end.