matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind1_rmap.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  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 "delayed_updating/syntax/path.ma".
  16 include "delayed_updating/notation/functions/black_righttriangle_1.ma".
  17 include "ground/relocation/tr_uni.ma".
  18 include "ground/relocation/tr_compose.ma".
  19
  20 (* BASIC UNWIND MAP FOR PATH ************************************************)
  21
  22 rec definition unwind1_rmap p on p: tr_map ≝
  23 match p with
  24 [ list_empty     ⇒ 𝐢
  25 | list_lcons l q ⇒
  26   match l with
  27   [ label_d n ⇒ (unwind1_rmap q)∘𝐮❨n❩
  28   | label_m   ⇒ unwind1_rmap q
  29   | label_L   ⇒ ⫯(unwind1_rmap q)
  30   | label_A   ⇒ unwind1_rmap q
  31   | label_S   ⇒ unwind1_rmap q
  32   ]
  33 ].
  34
  35 interpretation
  36   "basic unwind map (reversed path)"
  37   'BlackRightTriangle p = (unwind1_rmap p).
  38
  39 (* Basic constructions *******************************************************)
  40
  41 lemma unwind1_rmap_empty:
  42       (𝐢) = ▶(𝐞).
  43 // qed.
  44
  45 lemma unwind1_rmap_d_sn (p) (n:pnat):
  46       (▶p∘𝐮❨n❩) = ▶(𝗱n◗p).
  47 // qed.
  48
  49 lemma unwind1_rmap_m_sn (p):
  50       ▶p = ▶(𝗺◗p).
  51 // qed.
  52
  53 lemma unwind1_rmap_L_sn (p):
  54       (⫯▶p) = ▶(𝗟◗p).
  55 // qed.
  56
  57 lemma unwind1_rmap_A_sn (p):
  58       ▶p = ▶(𝗔◗p).
  59 // qed.
  60
  61 lemma unwind1_rmap_S_sn (p):
  62       ▶p = ▶(𝗦◗p).
  63 // qed.