helm/software/matita/contribs/procedural/Coq/ZArith/Zwf.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 (* $Id: Zwf.v,v 1.7 2003/11/29 17:28:46 herbelin Exp $ *)
  34
  35 include "ZArith/ZArith_base.ma".
  36
  37 include "Arith/Wf_nat.ma".
  38
  39 (* UNEXPORTED
  40 Open Local Scope Z_scope.
  41 *)
  42
  43 (*#* Well-founded relations on Z. *)
  44
  45 (*#* We define the following family of relations on [Z x Z]:
  46
  47     [x (Zwf c) y]   iff   [x < y & c <= y]
  48  *)
  49
  50 inline procedural "cic:/Coq/ZArith/Zwf/Zwf.con" as definition.
  51
  52 (*#* and we prove that [(Zwf c)] is well founded *)
  53
  54 (* UNEXPORTED
  55 Section wf_proof
  56 *)
  57
  58 (* UNEXPORTED
  59 cic:/Coq/ZArith/Zwf/wf_proof/c.var
  60 *)
  61
  62 (*#* The proof of well-foundness is classic: we do the proof by induction
  63     on a measure in nat, which is here [|x-c|] *)
  64
  65 inline procedural "cic:/Coq/ZArith/Zwf/wf_proof/f.con" "wf_proof__" as definition.
  66
  67 inline procedural "cic:/Coq/ZArith/Zwf/Zwf_well_founded.con" as lemma.
  68
  69 (* UNEXPORTED
  70 End wf_proof
  71 *)
  72
  73 (* UNEXPORTED
  74 Hint Resolve Zwf_well_founded: datatypes v62.
  75 *)
  76
  77 (*#* We also define the other family of relations:
  78
  79     [x (Zwf_up c) y]   iff   [y < x <= c]
  80  *)
  81
  82 inline procedural "cic:/Coq/ZArith/Zwf/Zwf_up.con" as definition.
  83
  84 (*#* and we prove that [(Zwf_up c)] is well founded *)
  85
  86 (* UNEXPORTED
  87 Section wf_proof_up
  88 *)
  89
  90 (* UNEXPORTED
  91 cic:/Coq/ZArith/Zwf/wf_proof_up/c.var
  92 *)
  93
  94 (*#* The proof of well-foundness is classic: we do the proof by induction
  95     on a measure in nat, which is here [|c-x|] *)
  96
  97 inline procedural "cic:/Coq/ZArith/Zwf/wf_proof_up/f.con" "wf_proof_up__" as definition.
  98
  99 inline procedural "cic:/Coq/ZArith/Zwf/Zwf_up_well_founded.con" as lemma.
 100
 101 (* UNEXPORTED
 102 End wf_proof_up
 103 *)
 104
 105 (* UNEXPORTED
 106 Hint Resolve Zwf_up_well_founded: datatypes v62.
 107 *)
 108