matita/matita/contribs/lambdadelta/ground/lib/stream_tls.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground/notation/functions/downspoonstar_3.ma".
  16 include "ground/lib/stream_hdtl.ma".
  17
  18 (* STREAMS ******************************************************************)
  19
  20 rec definition tls (A:Type[0]) (n:nat) on n: stream A → stream A ≝ ?.
  21 cases n -n [ #t @t | #n #t @tl @(tls … n t) ]
  22 defined.
  23
  24 interpretation "iterated tail (stram)" 'DownSpoonStar A n f = (tls A n f).
  25
  26 (* basic properties *********************************************************)
  27
  28 lemma tls_rew_O (A) (t): t = tls A 0 t.
  29 // qed.
  30
  31 lemma tls_rew_S (A) (n) (t): ⫰⫰*[n]t = tls A (↑n) t.
  32 // qed.
  33
  34 lemma tls_S1 (A) (n) (t): ⫰*[n]⫰t = tls A (↑n) t.
  35 #A #n elim n -n //
  36 qed.
  37
  38 lemma tls_eq_repl (A) (n): eq_stream_repl A (λt1,t2. ⫰*[n] t1 ≗ ⫰*[n] t2).
  39 #A #n elim n -n //
  40 #n #IH * #n1 #t1 * #n2 #t2 #H elim (eq_stream_inv_seq … H) /2 width=7 by/
  41 qed.