matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.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/unwind/unwind2_rmap_labels.ma".
  16 include "delayed_updating/unwind/nap.ma".
  17 include "delayed_updating/syntax/path_head_depth.ma".
  18 include "delayed_updating/syntax/path_height.ma".
  19
  20 (* UNWIND MAP FOR PATH ******************************************************)
  21
  22 (* Constructions with path_head *********************************************)
  23
  24 lemma unwind2_rmap_head_push (f) (p) (n):
  25       n + ♯(↳[n]p) = (▶[⫯f]↳[n]p)@↑❨n❩.
  26 #f #p elim p -p
  27 [ #n <path_head_empty <unwind2_rmap_labels_L <height_labels_L
  28   >tr_pushs_swap <tr_nap_pushs_lt //
  29 | #l #p #IH #n @(nat_ind_succ … n) -n //
  30   #n #_ cases l [ #m ]
  31   [ <unwind2_rmap_d_sn <path_head_d_sn <height_d_sn
  32     <nplus_assoc >IH -IH <tr_compose_nap //
  33   | <unwind2_rmap_m_sn <path_head_m_sn <height_m_sn //
  34   | <unwind2_rmap_L_sn <path_head_L_sn <height_L_sn
  35     <tr_nap_push <npred_succ //
  36   | <unwind2_rmap_A_sn <path_head_A_sn <height_A_sn //
  37   | <unwind2_rmap_S_sn <path_head_S_sn <height_S_sn //
  38   ]
  39 ]
  40 qed.