matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed_height.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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_closed.ma".
  16 include "delayed_updating/syntax/path_height.ma".
  17 include "delayed_updating/syntax/path_depth.ma".
  18
  19 (* CLOSED CONDITION FOR PATH ************************************************)
  20
  21 (* Destructions with height and depth ***************************************)
  22
  23 lemma path_closed_des_depth (o) (e) (q) (n):
  24       q ϵ 𝐂❨o,n,e❩ → ♯q + n = ♭q + e.
  25 #o #e #q #n #Hq elim Hq -q -n //
  26 #q #n #_ #IH
  27 <nplus_succ_dx <nplus_succ_sn //
  28 qed-.
  29
  30 lemma path_closed_des_succ_zero_depth (o) (q) (n):
  31       q ϵ 𝐂❨o,↑n,𝟎❩ → ♭q = ↑↓♭q.
  32 #o #q #n #Hq
  33 >(nplus_zero_dx (♭q))
  34 <(path_closed_des_depth … Hq) -Hq
  35 <nplus_succ_dx <npred_succ //
  36 qed-.