matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap.ma

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  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "delayed_updating/unwind/preunwind2_rmap.ma".
  16 include "delayed_updating/syntax/path.ma".
  17
  18 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
  19
  20 rec definition unwind2_rmap (f) (p) on p: tr_map ≝
  21 match p with
  22 [ list_empty     ⇒ f
  23 | list_lcons l q ⇒ ▶[unwind2_rmap f q]l
  24 ].
  25
  26 interpretation
  27   "tailed unwind (relocation map)"
  28   'BlackRightTriangle f p = (unwind2_rmap f p).
  29
  30 (* Basic constructions ******************************************************)
  31
  32 lemma unwind2_rmap_empty (f):
  33       f = ▶[f]𝐞.
  34 // qed.
  35
  36 lemma unwind2_rmap_rcons (f) (p) (l):
  37       ▶[▶[f]p]l = ▶[f](p◖l).
  38 // qed.
  39
  40 lemma unwind2_rmap_d_dx (f) (p) (k:pnat):
  41       ▶[f]p∘𝐮❨k❩ = ▶[f](p◖𝗱k).
  42 // qed.
  43
  44 lemma unwind2_rmap_m_dx (f) (p):
  45       ▶[f]p = ▶[f](p◖𝗺).
  46 // qed.
  47
  48 lemma unwind2_rmap_L_dx (f) (p):
  49       (⫯▶[f]p) = ▶[f](p◖𝗟).
  50 // qed.
  51
  52 lemma unwind2_rmap_A_dx (f) (p):
  53       ▶[f]p = ▶[f](p◖𝗔).
  54 // qed.
  55
  56 lemma unwind2_rmap_S_dx (f) (p):
  57       ▶[f]p = ▶[f](p◖𝗦).
  58 // qed.
  59
  60 (* Constructions with path_append *******************************************)
  61
  62 lemma unwind2_rmap_append (f) (p) (q):
  63       ▶[▶[f]p]q = ▶[f](p●q).
  64 #f #p #q elim q -q // #l #q #IH
  65 <unwind2_rmap_rcons <unwind2_rmap_rcons //
  66 qed.
  67
  68 (* Constructions with path_lcons ********************************************)
  69
  70 lemma unwind2_rmap_lcons (f) (p) (l):
  71       ▶[▶[f]l]p = ▶[f](l◗p).
  72 // qed.
  73
  74 lemma unwind2_rmap_d_sn (f) (p) (k:pnat):
  75       ▶[f∘𝐮❨k❩]p = ▶[f](𝗱k◗p).
  76 // qed.
  77
  78 lemma unwind2_rmap_m_sn (f) (p):
  79       ▶[f]p = ▶[f](𝗺◗p).
  80 // qed.
  81
  82 lemma unwind2_rmap_L_sn (f) (p):
  83       ▶[⫯f]p = ▶[f](𝗟◗p).
  84 // qed.
  85
  86 lemma unwind2_rmap_A_sn (f) (p):
  87       ▶[f]p = ▶[f](𝗔◗p).
  88 // qed.
  89
  90 lemma unwind2_rmap_S_sn (f) (p):
  91       ▶[f]p = ▶[f](𝗦◗p).
  92 // qed.