unfold Str_nth; simple induction n.
- intros s1 s2 H; case H; trivial with datatypes.
- intros m hypind.
simpl.
intros s1 s2 H.
apply hypind.
case H; trivial with datatypes.
Qed.

Theorem ntheq_eqst :
forall s1 s2:Stream,
(forall n:nat, Str_nth n s1 = Str_nth n s2) -> EqSt s1 s2.