helm/software/matita/contribs/procedural/Coq/ZArith/Wf_Z.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: Wf_Z.v,v 1.20.2.1 2004/07/16 19:31:20 herbelin Exp $ i*)
  34
  35 include "ZArith/BinInt.ma".
  36
  37 include "ZArith/Zcompare.ma".
  38
  39 include "ZArith/Zorder.ma".
  40
  41 include "ZArith/Znat.ma".
  42
  43 include "ZArith/Zmisc.ma".
  44
  45 include "Arith/Wf_nat.ma".
  46
  47 (* UNEXPORTED
  48 Open Local Scope Z_scope.
  49 *)
  50
  51 (*#* Our purpose is to write an induction shema for {0,1,2,...}
  52   similar to the [nat] schema (Theorem [Natlike_rec]). For that the
  53   following implications will be used :
  54 <<
  55  (n:nat)(Q n)==(n:nat)(P (inject_nat n)) ===> (x:Z)`x > 0) -> (P x)
  56
  57              /\
  58              ||
  59              ||
  60
  61   (Q O) (n:nat)(Q n)->(Q (S n)) <=== (P 0) (x:Z) (P x) -> (P (Zs x))
  62
  63                                 <=== (inject_nat (S n))=(Zs (inject_nat n))
  64
  65                                 <=== inject_nat_complete
  66 >>
  67   Then the  diagram will be closed and the theorem proved. *)
  68
  69 inline procedural "cic:/Coq/ZArith/Wf_Z/Z_of_nat_complete.con" as lemma.
  70
  71 inline procedural "cic:/Coq/ZArith/Wf_Z/ZL4_inf.con" as lemma.
  72
  73 inline procedural "cic:/Coq/ZArith/Wf_Z/Z_of_nat_complete_inf.con" as lemma.
  74
  75 inline procedural "cic:/Coq/ZArith/Wf_Z/Z_of_nat_prop.con" as lemma.
  76
  77 inline procedural "cic:/Coq/ZArith/Wf_Z/Z_of_nat_set.con" as lemma.
  78
  79 inline procedural "cic:/Coq/ZArith/Wf_Z/natlike_ind.con" as lemma.
  80
  81 inline procedural "cic:/Coq/ZArith/Wf_Z/natlike_rec.con" as lemma.
  82
  83 (* UNEXPORTED
  84 Section Efficient_Rec
  85 *)
  86
  87 (*#* [natlike_rec2] is the same as [natlike_rec], but with a different proof, designed
  88      to give a better extracted term. *)
  89
  90 (* UNAVAILABLE OBJECT: cic:/Coq/ZArith/Wf_Z/Efficient_Rec/R.con ***********)
  91
  92 inline procedural "cic:/Coq/ZArith/Wf_Z/Efficient_Rec/R.con" "Efficient_Rec__" as definition.
  93
  94 (* UNAVAILABLE OBJECT: cic:/Coq/ZArith/Wf_Z/Efficient_Rec/R_wf.con ********)
  95
  96 inline procedural "cic:/Coq/ZArith/Wf_Z/Efficient_Rec/R_wf.con" "Efficient_Rec__" as definition.
  97
  98 inline procedural "cic:/Coq/ZArith/Wf_Z/natlike_rec2.con" as lemma.
  99
 100 (*#* A variant of the previous using [Zpred] instead of [Zs]. *)
 101
 102 inline procedural "cic:/Coq/ZArith/Wf_Z/natlike_rec3.con" as lemma.
 103
 104 (*#* A more general induction principal using [Zlt]. *)
 105
 106 inline procedural "cic:/Coq/ZArith/Wf_Z/Z_lt_rec.con" as lemma.
 107
 108 inline procedural "cic:/Coq/ZArith/Wf_Z/Z_lt_induction.con" as lemma.
 109
 110 (* UNEXPORTED
 111 End Efficient_Rec
 112 *)
 113