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diff --git a/matita/matita/contribs/lambdadelta/ground_2/etc/relocation/trace.etc b/matita/matita/contribs/lambdadelta/ground_2/etc/relocation/trace.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 "ground_2/notation/functions/norm_1.ma".
-include "ground_2/lib/bool.ma".
-include "ground_2/lib/list.ma".
-
-(* RELOCATION TRACE *********************************************************)
-
-definition trace: Type[0] ≝ list bool.
-
-let rec colength (cs:trace) on cs ≝ match cs with
-[ nil       ⇒ 0
-| cons b tl ⇒ match b with [ true ⇒  ⫯(colength tl) | false ⇒ colength tl ] 
-].
-
-interpretation "colength (trace)"
-   'Norm cs = (colength cs).
-
-(* basic properties *********************************************************)
-
-lemma colength_empty: ∥◊∥ = 0.
-// qed.
-
-lemma colength_true: ∀cs. ∥Ⓣ@cs∥ = ⫯∥cs∥.
-// qed.
-
-lemma colength_false: ∀cs. ∥Ⓕ@cs∥ = ∥cs∥.
-// qed.
-
-lemma colength_cons: ∀cs1,cs2. ∥cs1∥ = ∥cs2∥ →
-                     ∀b. ∥b@cs1∥ = ∥b@cs2∥.
-#cs1 #cs2 #H * /2 width=1 by/
-qed.
-
-lemma colength_le: ∀cs. ∥cs∥ ≤ |cs|.
-#cs elim cs -cs //
-* /2 width=1 by le_S_S, le_S/
-qed.