matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_rmap.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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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/substitution/prelift_rmap.ma".
  16 include "delayed_updating/syntax/path.ma".
  17
  18 (* LIFT FOR RELOCATION MAP **************************************************)
  19
  20 rec definition lift_rmap (f) (p) on p: tr_map ≝
  21 match p with
  22 [ list_empty     ⇒ f
  23 | list_lcons l q ⇒ 🠢[lift_rmap f q]l
  24 ].
  25
  26 interpretation
  27   "lift (relocation map)"
  28   'RightTriangleArrow f p = (lift_rmap f p).
  29
  30 (* Basic constructions ******************************************************)
  31
  32 lemma lift_rmap_empty (f):
  33       f = 🠢[f]𝐞.
  34 // qed.
  35
  36 lemma lift_rmap_rcons (f) (p) (l):
  37       🠢[🠢[f]p]l = 🠢[f](p◖l).
  38 // qed.
  39
  40 lemma lift_rmap_d_dx (f) (p) (k:pnat):
  41       ⇂*[k](🠢[f]p) = 🠢[f](p◖𝗱k).
  42 // qed.
  43
  44 lemma lift_rmap_m_dx (f) (p):
  45       🠢[f]p = 🠢[f](p◖𝗺).
  46 // qed.
  47
  48 lemma lift_rmap_L_dx (f) (p):
  49       (⫯🠢[f]p) = 🠢[f](p◖𝗟).
  50 // qed.
  51
  52 lemma lift_rmap_A_dx (f) (p):
  53       🠢[f]p = 🠢[f](p◖𝗔).
  54 // qed.
  55
  56 lemma lift_rmap_S_dx (f) (p):
  57       🠢[f]p = 🠢[f](p◖𝗦).
  58 // qed.
  59
  60 (* Constructions with path_append *******************************************)
  61
  62 lemma lift_rmap_append (p) (q) (f):
  63       🠢[🠢[f]p]q = 🠢[f](p●q).
  64 #p #q elim q -q //
  65 qed.
  66
  67 (* Constructions with path_lcons ********************************************)
  68
  69 lemma lift_rmap_lcons (f) (p) (l):
  70       🠢[🠢[f]l]p = 🠢[f](l◗p).
  71 // qed.
  72
  73 lemma lift_rmap_d_sn (f) (p) (k:pnat):
  74       🠢[⇂*[k]f]p = 🠢[f](𝗱k◗p).
  75 // qed.
  76
  77 lemma lift_rmap_m_sn (f) (p):
  78       🠢[f]p = 🠢[f](𝗺◗p).
  79 // qed.
  80
  81 lemma lift_rmap_L_sn (f) (p):
  82       🠢[⫯f]p = 🠢[f](𝗟◗p).
  83 // qed.
  84
  85 lemma lift_rmap_A_sn (f) (p):
  86       🠢[f]p = 🠢[f](𝗔◗p).
  87 // qed.
  88
  89 lemma lift_rmap_S_sn (f) (p):
  90       🠢[f]p = 🠢[f](𝗦◗p).
  91 // qed.