matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_head_structure.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_head_depth.ma".
  16 include "delayed_updating/syntax/path_structure_labels.ma".
  17
  18 (* HEAD FOR PATH ************************************************************)
  19
  20 (* Constructions with structure *********************************************)
  21
  22 lemma path_head_structure_height (p) (n):
  23       ⊗↳[n]p = ↳[n+♯↳[n]p]⊗p.
  24 #p elim p -p //
  25 #l #p #IH #n @(nat_ind_succ … n) -n //
  26 #n #_ cases l [ #k ]
  27 [ <height_d_dx <structure_d_dx //
  28 | <structure_m_dx //
  29 | <structure_L_dx //
  30 | <height_A_dx <structure_A_dx <nplus_succ_sn <path_head_A_dx //
  31 | <height_S_dx <structure_S_dx <nplus_succ_sn <path_head_S_dx //
  32 ]
  33 qed.
  34
  35 lemma path_head_structure_depth (p) (n):
  36       ⊗↳[n]p = ↳[♭↳[n]p]⊗p.
  37 #p #n
  38 <path_head_depth //
  39 qed.