helm/software/matita/contribs/procedural/Coq/ZArith/Zmisc.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___,, *        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: Zmisc.v,v 1.20 2003/11/29 17:28:45 herbelin Exp $ i*)
  34
  35 include "ZArith/BinInt.ma".
  36
  37 include "ZArith/Zcompare.ma".
  38
  39 include "ZArith/Zorder.ma".
  40
  41 include "Bool/Bool.ma".
  42
  43 (* UNEXPORTED
  44 Open Local Scope Z_scope.
  45 *)
  46
  47 (*#*********************************************************************)
  48
  49 (*#* Iterators *)
  50
  51 (*#* [n]th iteration of the function [f] *)
  52
  53 inline procedural "cic:/Coq/ZArith/Zmisc/iter_nat.con" as definition.
  54
  55 inline procedural "cic:/Coq/ZArith/Zmisc/iter_pos.con" as definition.
  56
  57 inline procedural "cic:/Coq/ZArith/Zmisc/iter.con" as definition.
  58
  59 inline procedural "cic:/Coq/ZArith/Zmisc/iter_nat_plus.con" as theorem.
  60
  61 inline procedural "cic:/Coq/ZArith/Zmisc/iter_nat_of_P.con" as theorem.
  62
  63 inline procedural "cic:/Coq/ZArith/Zmisc/iter_pos_plus.con" as theorem.
  64
  65 (*#* Preservation of invariants : if [f : A->A] preserves the invariant [Inv],
  66     then the iterates of [f] also preserve it. *)
  67
  68 inline procedural "cic:/Coq/ZArith/Zmisc/iter_nat_invariant.con" as theorem.
  69
  70 inline procedural "cic:/Coq/ZArith/Zmisc/iter_pos_invariant.con" as theorem.
  71