matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed.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/syntax/path.ma".
  16 include "delayed_updating/notation/functions/class_c_1.ma".
  17 include "ground/lib/subset.ma".
  18
  19 include "delayed_updating/syntax/path_depth.ma".
  20 include "delayed_updating/syntax/path_height.ma".
  21
  22 (* CLOSED CONDITION FOR PATH ************************************************)
  23
  24 axiom pcc: relation2 nat path.
  25
  26 interpretation
  27   "closed condition (path)"
  28   'ClassC n = (pcc n).
  29
  30 (* Basic destructions *******************************************************)
  31
  32 axiom pcc_empty:
  33       (𝐞) ϵ 𝐂❨𝟎❩.
  34
  35 axiom pcc_d (p) (d) (n:pnat):
  36       p ϵ 𝐂❨d+n❩ → p◖𝗱n ϵ 𝐂❨d❩.
  37
  38 axiom pcc_L (p) (d):
  39       p ϵ 𝐂❨d❩ → p◖𝗟 ϵ 𝐂❨↑d❩.
  40
  41 axiom pcc_A (p) (d):
  42       p ϵ 𝐂❨d❩ → p◖𝗔 ϵ 𝐂❨d❩.
  43
  44 axiom pcc_S (p) (d):
  45       p ϵ 𝐂❨d❩ → p◖𝗦 ϵ 𝐂❨d❩.
  46
  47 axiom pcc_des_gen (p) (d):
  48       p ϵ 𝐂❨d❩ → d + ♯p = ❘p❘.