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[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / head / path_labels.etc
diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_labels.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_labels.etc
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "delayed_updating/syntax/path.ma".
-include "delayed_updating/notation/functions/power_2.ma".
-include "ground/arith/nat_succ_iter.ma".
-
-(* *)
-
-definition labels (l) (n:nat): path ā‰
-           ((list_lcons ? l)^n) (šž).
-
-interpretation
-  "labels (path)"
-  'Power l n = (labels l n).
-
-(* Basic constructions ******************************************************)
-
-lemma labels_unfold (l) (n):
-      ((list_lcons ? l)^n) (šž) = lāˆ—āˆ—n.
-// qed.
-
-lemma labels_zero (l):
-      (šž) = lāˆ—āˆ—šŸŽ.
-// qed.
-
-lemma labels_succ (l) (n):
-      (lāˆ—āˆ—n)ā—–l = lāˆ—āˆ—(ā†‘n).
-#l #n
-<labels_unfold <labels_unfold <niter_succ //
-qed.
-
-(* Basic inversions *********************************************************)
-
-lemma eq_inv_empty_labels (l) (n):
-      (šž) = lāˆ—āˆ—n ā†’ šŸŽ = n.
-#l #n @(nat_ind_succ ā€¦ n) -n //
-#n #_ <labels_succ #H0 destruct
-qed-.