matita/matita/contribs/lambdadelta/delayed_updating/etc/dhd/path_dhd_structure.etc

   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_dhd.ma".
  16 include "delayed_updating/syntax/path_structure.ma".
  17 include "delayed_updating/syntax/path_depth.ma".
  18
  19 (* HEAD BY DEPTH FOR PATH ***************************************************)
  20
  21 (* Constructions with structure *********************************************)
  22
  23 lemma path_dhd_structure_L_sn (p) (q):
  24       let r ≝ 𝗟◗p in
  25       ⊗r = ↳⧣[♭⊗r]((⊗r)●q).
  26 #p elim p -p //
  27 * [ #n ] #p #IH #q //
  28   [ <structure_L_sn //
  29   | <structure_A_sn <list_append_lcons_sn
  30     <path_head_A_sn //
  31   | <structure_S_sn //
  32   ]
  33 ]
  34 *)