matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_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/notation/functions/uparrow_2.ma".
  16 include "delayed_updating/syntax/label.ma".
  17 include "ground/relocation/tr_pn.ma".
  18 include "ground/lib/stream_tls.ma".
  19
  20 (* PRELIFT FOR RELOCATION MAP ***********************************************)
  21
  22 definition prelift_rmap (f) (l): tr_map ≝
  23 match l with
  24 [ label_d k ⇒ ⇂*[k]f
  25 | label_m   ⇒ f
  26 | label_L   ⇒ ⫯f
  27 | label_A   ⇒ f
  28 | label_S   ⇒ f
  29 ].
  30
  31 interpretation
  32   "prelift (relocation map)"
  33   'UpArrow l f = (prelift_rmap f l).
  34
  35 (* Basic constructions ******************************************************)
  36
  37 lemma prelift_rmap_d (f) (k:pnat):
  38       ⇂*[k]f = ↑[𝗱k]f.
  39 // qed.
  40
  41 lemma prelift_rmap_m (f):
  42       f = ↑[𝗺]f.
  43 // qed.
  44
  45 lemma prelift_rmap_L (f):
  46       (⫯f) = ↑[𝗟]f.
  47 // qed.
  48
  49 lemma prelift_rmap_A (f):
  50       f = ↑[𝗔]f.
  51 // qed.
  52
  53 lemma prelift_rmap_S (f):
  54       f = ↑[𝗦]f.
  55 // qed.