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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "delayed_updating/notation/functions/uparrow_2.ma".
  16 include "delayed_updating/syntax/label.ma".
  17 include "ground/relocation/tr_pap.ma".
  18
  19 (* PRELIFT FOR LABEL ********************************************************)
  20
  21 definition prelift_label (f) (l): label ≝
  22 match l with
  23 [ label_d n ⇒ 𝗱(f＠⧣❨n❩)
  24 | label_m   ⇒ 𝗺
  25 | label_L   ⇒ 𝗟
  26 | label_A   ⇒ 𝗔
  27 | label_S   ⇒ 𝗦
  28 ].
  29
  30 interpretation
  31   "prelift (label)"
  32   'UpArrow f l = (prelift_label f l).
  33
  34 (* Basic constructions ******************************************************)
  35
  36 lemma prelift_label_d (f) (n):
  37       (𝗱(f＠⧣❨n❩)) = ↑[f]𝗱n.
  38 // qed.
  39
  40 lemma prelift_label_m (f):
  41       (𝗺) = ↑[f]𝗺.
  42 // qed.
  43
  44 lemma prelift_label_L (f):
  45       (𝗟) = ↑[f]𝗟.
  46 // qed.
  47
  48 lemma prelift_label_A (f):
  49       (𝗔) = ↑[f]𝗔.
  50 // qed.
  51
  52 lemma prelift_label_S (f):
  53       (𝗦) = ↑[f]𝗦.
  54 // qed.