1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "ground/notation/functions/downharpoonrightstar_3.ma".
16 include "ground/lib/stream_hdtl.ma".
17 include "ground/arith/nat_succ_iter.ma".
19 (* ITERATED TAIL FOR STREAMS ************************************************)
21 definition stream_tls (A) (n): stream A → stream A ≝
25 "iterated tail (strams)"
26 'DownHarpoonRightStar A n f = (stream_tls A n f).
28 (* Basic constructions ******************************************************)
30 lemma stream_tls_zero (A) (t):
34 lemma stream_tls_tl (A) (n) (t):
35 (⇂⇂*[n]t) = ⇂*{A}[n]⇂t.
37 @(niter_appl … (stream_tl …))
40 lemma stream_tls_succ (A) (n) (t):
41 (⇂⇂*[n]t) = ⇂*{A}[↑n]t.
43 @(niter_succ … (stream_tl …))
46 lemma stream_tls_swap (A) (n) (t):
47 (⇂*[n]⇂t) = ⇂*{A}[↑n]t.