matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_labels.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.ma".
  16 include "delayed_updating/notation/functions/power_2.ma".
  17 include "ground/arith/nat_succ_iter.ma".
  18
  19 (* *)
  20
  21 definition labels (l) (n:nat): path ≝
  22            ((list_lcons ? l)^n) (𝐞).
  23
  24 interpretation
  25   "labels (path)"
  26   'Power l n = (labels l n).
  27
  28 (* Basic constructions ******************************************************)
  29
  30 lemma labels_unfold (l) (n):
  31       ((list_lcons ? l)^n) (𝐞) = l∗∗n.
  32 // qed.
  33
  34 lemma labels_zero (l):
  35       (𝐞) = l∗∗𝟎.
  36 // qed.
  37
  38 lemma labels_succ (l) (n):
  39       (l∗∗n)◖l = l∗∗(↑n).
  40 #l #n
  41 <labels_unfold <labels_unfold <niter_succ //
  42 qed.
  43
  44 (* Basic inversions *********************************************************)
  45
  46 lemma eq_inv_empty_labels (l) (n):
  47       (𝐞) = l∗∗n → 𝟎 = n.
  48 #l #n @(nat_ind_succ … n) -n //
  49 #n #_ <labels_succ #H0 destruct
  50 qed-.