matita/matita/contribs/lambdadelta/ground/relocation/pr_tls.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "ground/notation/functions/downspoonstar_2.ma".
  16 include "ground/lib/stream_tls.ma".
  17 include "ground/relocation/pr_tl.ma".
  18
  19 (* ITERATED TAIL FOR PARTIAL RELOCATION MAPS ********************************)
  20
  21 (*** tls *)
  22 definition pr_tls (n) (f:pr_map) ≝ ⇂*[n]f.
  23
  24 interpretation
  25   "iterated tail (partial relocation maps)"
  26   'DownSpoonStar n f = (pr_tls n f).
  27
  28 (* Basic constructions (specific) *******************************************)
  29
  30 (*** tls_O *)
  31 lemma pr_tls_zero (f): f = ⫰*[𝟎] f.
  32 // qed.
  33
  34 (*** tls_swap *)
  35 lemma pr_tls_tl (n) (f): ⫰⫰*[n] f = ⫰*[n] ⫰f.
  36 /2 width=1 by stream_tls_tl/ qed.
  37
  38 (*** tls_S *)
  39 lemma pr_tls_succ (n) (f): ⫰⫰*[n] f = ⫰*[↑n] f.
  40 /2 width=1 by stream_tls_succ/ qed.
  41
  42 (*** tls_xn *)
  43 lemma pr_tls_swap (n) (f): ⫰*[n] ⫰f = ⫰*[↑n] f.
  44 // qed.