ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / etc / relocation / trace.etc

diff --git a/matita/matita/contribs/lambdadelta/ground/etc/relocation/trace.etc b/matita/matita/contribs/lambdadelta/ground/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.