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_at_most_n_stream {A B: Type}: forall (f: A -> B) (h: stream A) (n: nat),
is_at_most_n_stream n h <-> is_at_most_n_stream n (stream_map f h).