--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "ground_2/notation/functions/downspoonstar_3.ma".
+include "ground_2/lib/stream_hdtl.ma".
+
+(* STREAMS ******************************************************************)
+
+rec definition tls (A:Type[0]) (n:nat) on n: stream A → stream A ≝ ?.
+cases n -n [ #t @t | #n #t @tl @(tls … n t) ]
+defined.
+
+interpretation "iterated tail (stram)" 'DownSpoonStar A n f = (tls A n f).
+
+(* basic properties *********************************************************)
+
+lemma tls_rew_O (A) (t): t = tls A 0 t.
+// qed.
+
+lemma tls_rew_S (A) (n) (t): ⫰⫰*[n]t = tls A (↑n) t.
+// qed.
+
+lemma tls_S1 (A) (n) (t): ⫰*[n]⫰t = tls A (↑n) t.
+#A #n elim n -n //
+qed.
+
+lemma tls_eq_repl (A) (n): eq_stream_repl A (λt1,t2. ⫰*[n] t1 ≗ ⫰*[n] t2).
+#A #n elim n -n //
+#n #IH * #n1 #t1 * #n2 #t2 #H elim (eq_stream_inv_seq … H) /2 width=7 by/
+qed.