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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  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___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  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: Zabs.v,v 1.4.2.1 2004/07/16 19:31:21 herbelin Exp $ i*)
  34
  35 (*#* Binary Integers (Pierre Cr\233\gut (CNET, Lannion, France) *)
  36
  37 include "Arith/Arith.ma".
  38
  39 include "NArith/BinPos.ma".
  40
  41 include "ZArith/BinInt.ma".
  42
  43 include "ZArith/Zorder.ma".
  44
  45 include "ZArith/ZArith_dec.ma".
  46
  47 (* UNEXPORTED
  48 Open Local Scope Z_scope.
  49 *)
  50
  51 (*#*********************************************************************)
  52
  53 (*#* Properties of absolute value *)
  54
  55 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_eq.con" as lemma.
  56
  57 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_non_eq.con" as lemma.
  58
  59 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_Zopp.con" as theorem.
  60
  61 (*#* Proving a property of the absolute value by cases *)
  62
  63 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_ind.con" as lemma.
  64
  65 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_intro.con" as theorem.
  66
  67 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_dec.con" as definition.
  68
  69 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_pos.con" as lemma.
  70
  71 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_eq_case.con" as theorem.
  72
  73 (*#* Triangular inequality *)
  74
  75 (* UNEXPORTED
  76 Hint Local Resolve Zle_neg_pos: zarith.
  77 *)
  78
  79 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_triangle.con" as theorem.
  80
  81 (*#* Absolute value and multiplication *)
  82
  83 inline procedural "cic:/Coq/ZArith/Zabs/Zsgn_Zabs.con" as lemma.
  84
  85 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_Zsgn.con" as lemma.
  86
  87 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_Zmult.con" as theorem.
  88
  89 (*#* absolute value in nat is compatible with order *)
  90
  91 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_nat_lt.con" as lemma.
  92