helm/software/matita/contribs/procedural/Coq/Arith/Gt.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: Gt.v,v 1.8.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 include "Arith/Le.ma".
  36
  37 include "Arith/Lt.ma".
  38
  39 include "Arith/Plus.ma".
  40
  41 (* UNEXPORTED
  42 Open Local Scope nat_scope.
  43 *)
  44
  45 (* UNEXPORTED
  46 Implicit Types m n p : nat.
  47 *)
  48
  49 (*#* Order and successor *)
  50
  51 inline procedural "cic:/Coq/Arith/Gt/gt_Sn_O.con" as theorem.
  52
  53 (* UNEXPORTED
  54 Hint Resolve gt_Sn_O: arith v62.
  55 *)
  56
  57 inline procedural "cic:/Coq/Arith/Gt/gt_Sn_n.con" as theorem.
  58
  59 (* UNEXPORTED
  60 Hint Resolve gt_Sn_n: arith v62.
  61 *)
  62
  63 inline procedural "cic:/Coq/Arith/Gt/gt_n_S.con" as theorem.
  64
  65 (* UNEXPORTED
  66 Hint Resolve gt_n_S: arith v62.
  67 *)
  68
  69 inline procedural "cic:/Coq/Arith/Gt/gt_S_n.con" as lemma.
  70
  71 (* UNEXPORTED
  72 Hint Immediate gt_S_n: arith v62.
  73 *)
  74
  75 inline procedural "cic:/Coq/Arith/Gt/gt_S.con" as theorem.
  76
  77 inline procedural "cic:/Coq/Arith/Gt/gt_pred.con" as lemma.
  78
  79 (* UNEXPORTED
  80 Hint Immediate gt_pred: arith v62.
  81 *)
  82
  83 (*#* Irreflexivity *)
  84
  85 inline procedural "cic:/Coq/Arith/Gt/gt_irrefl.con" as lemma.
  86
  87 (* UNEXPORTED
  88 Hint Resolve gt_irrefl: arith v62.
  89 *)
  90
  91 (*#* Asymmetry *)
  92
  93 inline procedural "cic:/Coq/Arith/Gt/gt_asym.con" as lemma.
  94
  95 (* UNEXPORTED
  96 Hint Resolve gt_asym: arith v62.
  97 *)
  98
  99 (*#* Relating strict and large orders *)
 100
 101 inline procedural "cic:/Coq/Arith/Gt/le_not_gt.con" as lemma.
 102
 103 (* UNEXPORTED
 104 Hint Resolve le_not_gt: arith v62.
 105 *)
 106
 107 inline procedural "cic:/Coq/Arith/Gt/gt_not_le.con" as lemma.
 108
 109 (* UNEXPORTED
 110 Hint Resolve gt_not_le: arith v62.
 111 *)
 112
 113 inline procedural "cic:/Coq/Arith/Gt/le_S_gt.con" as theorem.
 114
 115 (* UNEXPORTED
 116 Hint Immediate le_S_gt: arith v62.
 117 *)
 118
 119 inline procedural "cic:/Coq/Arith/Gt/gt_S_le.con" as lemma.
 120
 121 (* UNEXPORTED
 122 Hint Immediate gt_S_le: arith v62.
 123 *)
 124
 125 inline procedural "cic:/Coq/Arith/Gt/gt_le_S.con" as lemma.
 126
 127 (* UNEXPORTED
 128 Hint Resolve gt_le_S: arith v62.
 129 *)
 130
 131 inline procedural "cic:/Coq/Arith/Gt/le_gt_S.con" as lemma.
 132
 133 (* UNEXPORTED
 134 Hint Resolve le_gt_S: arith v62.
 135 *)
 136
 137 (*#* Transitivity *)
 138
 139 inline procedural "cic:/Coq/Arith/Gt/le_gt_trans.con" as theorem.
 140
 141 inline procedural "cic:/Coq/Arith/Gt/gt_le_trans.con" as theorem.
 142
 143 inline procedural "cic:/Coq/Arith/Gt/gt_trans.con" as lemma.
 144
 145 inline procedural "cic:/Coq/Arith/Gt/gt_trans_S.con" as theorem.
 146
 147 (* UNEXPORTED
 148 Hint Resolve gt_trans_S le_gt_trans gt_le_trans: arith v62.
 149 *)
 150
 151 (*#* Comparison to 0 *)
 152
 153 inline procedural "cic:/Coq/Arith/Gt/gt_O_eq.con" as theorem.
 154
 155 (*#* Simplification and compatibility *)
 156
 157 inline procedural "cic:/Coq/Arith/Gt/plus_gt_reg_l.con" as lemma.
 158
 159 inline procedural "cic:/Coq/Arith/Gt/plus_gt_compat_l.con" as lemma.
 160
 161 (* UNEXPORTED
 162 Hint Resolve plus_gt_compat_l: arith v62.
 163 *)
 164