Section Streams.
Variable A : Type.
Notation Stream := (Stream A).
Definition hd (x:Stream) := match x with
| Cons a _ => a
end.
Definition tl (x:Stream) := match x with
| Cons _ s => s
end.
Fixpoint Str_nth_tl (n:nat) (s:Stream) : Stream :=
match n with
| O => s
| S m => Str_nth_tl m (tl s)
end.
Definition Str_nth (n:nat) (s:Stream) : A := hd (Str_nth_tl n s).
Hint Resolve tl_nth_tl: datatypes.
simple induction n; simpl; intros; auto with datatypes.
rewrite <- H.
rewrite tl_nth_tl; trivial with datatypes.
Qed.

Lemma Str_nth_plus :
forall (n m:nat) (s:Stream), Str_nth n (Str_nth_tl m s) = Str_nth (n + m) s.