matita/matita/contribs/lambdadelta/ground/etc/relocation/trace.etc

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "ground_2/notation/functions/norm_1.ma".
  16 include "ground_2/lib/bool.ma".
  17 include "ground_2/lib/list.ma".
  18
  19 (* RELOCATION TRACE *********************************************************)
  20
  21 definition trace: Type[0] ≝ list bool.
  22
  23 let rec colength (cs:trace) on cs ≝ match cs with
  24 [ nil       ⇒ 0
  25 | cons b tl ⇒ match b with [ true ⇒  ⫯(colength tl) | false ⇒ colength tl ]
  26 ].
  27
  28 interpretation "colength (trace)"
  29    'Norm cs = (colength cs).
  30
  31 (* basic properties *********************************************************)
  32
  33 lemma colength_empty: ∥◊∥ = 0.
  34 // qed.
  35
  36 lemma colength_true: ∀cs. ∥Ⓣ@cs∥ = ⫯∥cs∥.
  37 // qed.
  38
  39 lemma colength_false: ∀cs. ∥Ⓕ@cs∥ = ∥cs∥.
  40 // qed.
  41
  42 lemma colength_cons: ∀cs1,cs2. ∥cs1∥ = ∥cs2∥ →
  43                      ∀b. ∥b@cs1∥ = ∥b@cs2∥.
  44 #cs1 #cs2 #H * /2 width=1 by/
  45 qed.
  46
  47 lemma colength_le: ∀cs. ∥cs∥ ≤ |cs|.
  48 #cs elim cs -cs //
  49 * /2 width=1 by le_S_S, le_S/
  50 qed.