matita/matita/contribs/lambdadelta/delayed_updating/unwind/preunwind2_rmap.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 "delayed_updating/syntax/label.ma".
  16 include "delayed_updating/notation/functions/black_righttriangle_2.ma".
  17 include "ground/relocation/tr_uni.ma".
  18 include "ground/relocation/tr_compose.ma".
  19
  20 (* TAILED PREUNWIND FOR RELOCATION MAP **************************************)
  21
  22 definition preunwind2_rmap (f) (l): tr_map ≝
  23 match l with
  24 [ label_d k ⇒ f∘𝐮❨k❩
  25 | label_m   ⇒ f
  26 | label_L   ⇒ ⫯f
  27 | label_A   ⇒ f
  28 | label_S   ⇒ f
  29 ].
  30
  31 interpretation
  32   "tailed preunwind (relocation map)"
  33   'BlackRightTriangle f l = (preunwind2_rmap f l).
  34
  35 (* Basic constructions ******************************************************)
  36
  37 lemma preunwind2_rmap_d (f) (k:pnat):
  38       f∘𝐮❨k❩ = ▶[f]𝗱k.
  39 // qed.
  40
  41 lemma preunwind2_rmap_m (f):
  42       f = ▶[f]𝗺.
  43 // qed.
  44
  45 lemma preunwind2_rmap_L (f):
  46       (⫯f) = ▶[f]𝗟.
  47 // qed.
  48
  49 lemma preunwind2_rmap_A (f):
  50       f = ▶[f]𝗔.
  51 // qed.
  52
  53 lemma preunwind2_rmap_S (f):
  54       f = ▶[f]𝗦.
  55 // qed.