helm/software/matita/contribs/procedural/Coq/Arith/Le.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 include "Init/Prelude.ma".
  20
  21 (*#***********************************************************************)
  22
  23 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  24
  25 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  26
  27 (*   \VV/  **************************************************************)
  28
  29 (*    //   *      This file is distributed under the terms of the       *)
  30
  31 (*         *       GNU Lesser General Public License Version 2.1        *)
  32
  33 (*#***********************************************************************)
  34
  35 (*i $Id: Le.v,v 1.14.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  36
  37 (*#* Order on natural numbers *)
  38
  39 (* UNEXPORTED
  40 Open Local Scope nat_scope.
  41 *)
  42
  43 (* UNEXPORTED
  44 Implicit Types m n p : nat.
  45 *)
  46
  47 (*#* Reflexivity *)
  48
  49 inline procedural "cic:/Coq/Arith/Le/le_refl.con" as theorem.
  50
  51 (*#* Transitivity *)
  52
  53 inline procedural "cic:/Coq/Arith/Le/le_trans.con" as theorem.
  54
  55 (* UNEXPORTED
  56 Hint Resolve le_trans: arith v62.
  57 *)
  58
  59 (*#* Order, successor and predecessor *)
  60
  61 inline procedural "cic:/Coq/Arith/Le/le_n_S.con" as theorem.
  62
  63 inline procedural "cic:/Coq/Arith/Le/le_n_Sn.con" as theorem.
  64
  65 inline procedural "cic:/Coq/Arith/Le/le_O_n.con" as theorem.
  66
  67 (* UNEXPORTED
  68 Hint Resolve le_n_S le_n_Sn le_O_n le_n_S: arith v62.
  69 *)
  70
  71 inline procedural "cic:/Coq/Arith/Le/le_pred_n.con" as theorem.
  72
  73 (* UNEXPORTED
  74 Hint Resolve le_pred_n: arith v62.
  75 *)
  76
  77 inline procedural "cic:/Coq/Arith/Le/le_Sn_le.con" as theorem.
  78
  79 (* UNEXPORTED
  80 Hint Immediate le_Sn_le: arith v62.
  81 *)
  82
  83 inline procedural "cic:/Coq/Arith/Le/le_S_n.con" as theorem.
  84
  85 (* UNEXPORTED
  86 Hint Immediate le_S_n: arith v62.
  87 *)
  88
  89 inline procedural "cic:/Coq/Arith/Le/le_pred.con" as theorem.
  90
  91 (*#* Comparison to 0 *)
  92
  93 inline procedural "cic:/Coq/Arith/Le/le_Sn_O.con" as theorem.
  94
  95 (* UNEXPORTED
  96 Hint Resolve le_Sn_O: arith v62.
  97 *)
  98
  99 inline procedural "cic:/Coq/Arith/Le/le_n_O_eq.con" as theorem.
 100
 101 (* UNEXPORTED
 102 Hint Immediate le_n_O_eq: arith v62.
 103 *)
 104
 105 (*#* Negative properties *)
 106
 107 inline procedural "cic:/Coq/Arith/Le/le_Sn_n.con" as theorem.
 108
 109 (* UNEXPORTED
 110 Hint Resolve le_Sn_n: arith v62.
 111 *)
 112
 113 (*#* Antisymmetry *)
 114
 115 inline procedural "cic:/Coq/Arith/Le/le_antisym.con" as theorem.
 116
 117 (* UNEXPORTED
 118 Hint Immediate le_antisym: arith v62.
 119 *)
 120
 121 (*#* A different elimination principle for the order on natural numbers *)
 122
 123 inline procedural "cic:/Coq/Arith/Le/le_elim_rel.con" as lemma.
 124