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 ⇒ ↑[l](lift_rmap f q)
  24 ].
  25
  26 interpretation
  27   "lift (relocation map)"
  28   'UpArrow p f = (lift_rmap f p).
  29
  30 (* Basic constructions ******************************************************)
  31
  32 lemma lift_rmap_empty (f):
  33       f = ↑[𝐞]f.
  34 // qed.
  35
  36 lemma lift_rmap_rcons (f) (p) (l):
  37       ↑[l]↑[p]f = ↑[p◖l]f.
  38 // qed.
  39
  40 lemma lift_rmap_d_dx (f) (p) (k:pnat):
  41       ⇂*[k](↑[p]f) = ↑[p◖𝗱k]f.
  42 // qed.
  43
  44 lemma lift_rmap_m_dx (f) (p):
  45       ↑[p]f = ↑[p◖𝗺]f.
  46 // qed.
  47
  48 lemma lift_rmap_L_dx (f) (p):
  49       (⫯↑[p]f) = ↑[p◖𝗟]f.
  50 // qed.
  51
  52 lemma lift_rmap_A_dx (f) (p):
  53       ↑[p]f = ↑[p◖𝗔]f.
  54 // qed.
  55
  56 lemma lift_rmap_S_dx (f) (p):
  57       ↑[p]f = ↑[p◖𝗦]f.
  58 // qed.
  59
  60 (* Constructions with path_append *******************************************)
  61
  62 lemma lift_rmap_append (p) (q) (f):
  63       ↑[q]↑[p]f = ↑[p●q]f.
  64 #p #q elim q -q //
  65 qed.
  66
  67 (* Constructions with path_lcons ********************************************)
  68
  69 lemma lift_rmap_lcons (f) (p) (l):
  70       ↑[p]↑[l]f = ↑[l◗p]f.
  71 // qed.
  72
  73 lemma lift_rmap_d_sn (f) (p) (k:pnat):
  74       ↑[p](⇂*[k]f) = ↑[𝗱k◗p]f.
  75 // qed.
  76
  77 lemma lift_rmap_m_sn (f) (p):
  78       ↑[p]f = ↑[𝗺◗p]f.
  79 // qed.
  80
  81 lemma lift_rmap_L_sn (f) (p):
  82       ↑[p](⫯f) = ↑[𝗟◗p]f.
  83 // qed.
  84
  85 lemma lift_rmap_A_sn (f) (p):
  86       ↑[p]f = ↑[𝗔◗p]f.
  87 // qed.
  88
  89 lemma lift_rmap_S_sn (f) (p):
  90       ↑[p]f = ↑[𝗦◗p]f.
  91 // qed.