matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure_depth.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/syntax/path_structure.ma".
  16 include "delayed_updating/syntax/path_depth.ma".
  17
  18 (* STRUCTURE FOR PATH *******************************************************)
  19
  20 (* Constructions with depth *************************************************)
  21
  22 lemma depth_structure (p):
  23       ❘p❘ = ❘⊗p❘.
  24 #p elim p -p //
  25 * [ #n ] #p #IH //
  26 [ <structure_L_sn <depth_L_sn <depth_L_sn //
  27 | <structure_A_sn <depth_A_sn <depth_A_sn //
  28 | <structure_S_sn <depth_S_sn <depth_S_sn //
  29 ]
  30 qed.