matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed_structure.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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  14
  15 include "delayed_updating/syntax/path_closed_height.ma".
  16 include "delayed_updating/syntax/path_structure.ma".
  17
  18 (* CLOSED CONDITION FOR PATH ************************************************)
  19
  20 (* Constructions with structure *********************************************)
  21
  22 lemma path_closed_structure_height (p) (n):
  23       p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♯p+n❩.
  24 #p #n #Hn elim Hn -Hn //
  25 #p #n #_ #IH [ <nplus_succ_dx ]
  26 /2 width=1 by pcc_L_dx, pcc_A_dx, pcc_S_dx/
  27 qed.
  28
  29 lemma path_closed_structure_depth (p) (n):
  30       p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♭p❩.
  31 #p #n #Hp <path_closed_depth
  32 /2 width=3 by path_closed_structure_height/
  33 qed.