matita/matita/contribs/lambdadelta/ground/relocation/tr_pn.ma

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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 "ground/relocation/tr_map.ma".
  16
  17 (* PUSH AND NEXT FOR TOTAL RELOCATION MAPS **********************************)
  18
  19 definition tr_push: tr_map → tr_map ≝
  20            λf. 𝟏⨮f.
  21
  22 interpretation
  23   "push (total relocation maps)"
  24   'UpSpoon f = (tr_push f).
  25
  26 definition tr_next: tr_map → tr_map.
  27 * #p #f @(↑p⨮f)
  28 defined.
  29
  30 interpretation
  31   "next (total relocation maps)"
  32   'UpArrow f = (tr_next f).
  33
  34 (* Basic constructions ******************************************************)
  35
  36 lemma tr_push_unfold (f): 𝟏⨮f = ⫯f.
  37 // qed.
  38
  39 lemma tr_next_unfold (f): ∀p. (↑p)⨮f = ↑(p⨮f).
  40 // qed.
  41
  42 (* Constructions with tr_inj ************************************************)
  43
  44 lemma tr_inj_push (f): ⫯𝐭❨f❩ = 𝐭❨⫯f❩.
  45 // qed.
  46
  47 lemma tr_inj_next (f): ↑𝐭❨f❩ = 𝐭❨↑f❩.
  48 * //
  49 qed.
  50
  51 (* Basic eliminations *******************************************************)
  52
  53 lemma tr_map_split (f:tr_map):
  54       ∨∨ ∃g. ⫯g = f
  55        | ∃g. ↑g = f.
  56 * *
  57 /3 width=2 by ex_intro, or_introl, or_intror/
  58 qed-.