helm/software/matita/contribs/procedural/Coq/ZArith/Zeven.mma

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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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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "Coq.ma".
  18
  19 (*#**********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
  22
  23 (* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
  24
  25 (*   \VV/  *************************************************************)
  26
  27 (*    //   *      This file is distributed under the terms of the      *)
  28
  29 (*         *       GNU Lesser General Public License Version 2.1       *)
  30
  31 (*#**********************************************************************)
  32
  33 (*i $Id: Zeven.v,v 1.3 2003/11/29 17:28:45 herbelin Exp $ i*)
  34
  35 include "ZArith/BinInt.ma".
  36
  37 (*#*********************************************************************)
  38
  39 (*#* About parity: even and odd predicates on Z, division by 2 on Z *)
  40
  41 (*#*********************************************************************)
  42
  43 (*#* [Zeven], [Zodd], [Zdiv2] and their related properties *)
  44
  45 inline procedural "cic:/Coq/ZArith/Zeven/Zeven.con" as definition.
  46
  47 inline procedural "cic:/Coq/ZArith/Zeven/Zodd.con" as definition.
  48
  49 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_bool.con" as definition.
  50
  51 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_bool.con" as definition.
  52
  53 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_odd_dec.con" as definition.
  54
  55 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_dec.con" as definition.
  56
  57 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_dec.con" as definition.
  58
  59 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_not_Zodd.con" as lemma.
  60
  61 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_not_Zeven.con" as lemma.
  62
  63 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_Sn.con" as lemma.
  64
  65 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_Sn.con" as lemma.
  66
  67 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_pred.con" as lemma.
  68
  69 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_pred.con" as lemma.
  70
  71 (* UNEXPORTED
  72 Hint Unfold Zeven Zodd: zarith.
  73 *)
  74
  75 (*#*********************************************************************)
  76
  77 (*#* [Zdiv2] is defined on all [Z], but notice that for odd negative
  78     integers it is not the euclidean quotient: in that case we have [n =
  79     2*(n/2)-1] *)
  80
  81 inline procedural "cic:/Coq/ZArith/Zeven/Zdiv2.con" as definition.
  82
  83 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_div2.con" as lemma.
  84
  85 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_div2.con" as lemma.
  86
  87 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_div2_neg.con" as lemma.
  88
  89 inline procedural "cic:/Coq/ZArith/Zeven/Z_modulo_2.con" as lemma.
  90
  91 inline procedural "cic:/Coq/ZArith/Zeven/Zsplit2.con" as lemma.
  92