helm/software/matita/contribs/procedural/Coq/Arith/Le.mma

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   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: Le.v,v 1.14.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 (*#* Order on natural numbers *)
  36
  37 (* UNEXPORTED
  38 Open Local Scope nat_scope.
  39 *)
  40
  41 (* UNEXPORTED
  42 Implicit Types m n p : nat.
  43 *)
  44
  45 (*#* Reflexivity *)
  46
  47 inline procedural "cic:/Coq/Arith/Le/le_refl.con" as theorem.
  48
  49 (*#* Transitivity *)
  50
  51 inline procedural "cic:/Coq/Arith/Le/le_trans.con" as theorem.
  52
  53 (* UNEXPORTED
  54 Hint Resolve le_trans: arith v62.
  55 *)
  56
  57 (*#* Order, successor and predecessor *)
  58
  59 inline procedural "cic:/Coq/Arith/Le/le_n_S.con" as theorem.
  60
  61 inline procedural "cic:/Coq/Arith/Le/le_n_Sn.con" as theorem.
  62
  63 inline procedural "cic:/Coq/Arith/Le/le_O_n.con" as theorem.
  64
  65 (* UNEXPORTED
  66 Hint Resolve le_n_S le_n_Sn le_O_n le_n_S: arith v62.
  67 *)
  68
  69 inline procedural "cic:/Coq/Arith/Le/le_pred_n.con" as theorem.
  70
  71 (* UNEXPORTED
  72 Hint Resolve le_pred_n: arith v62.
  73 *)
  74
  75 inline procedural "cic:/Coq/Arith/Le/le_Sn_le.con" as theorem.
  76
  77 (* UNEXPORTED
  78 Hint Immediate le_Sn_le: arith v62.
  79 *)
  80
  81 inline procedural "cic:/Coq/Arith/Le/le_S_n.con" as theorem.
  82
  83 (* UNEXPORTED
  84 Hint Immediate le_S_n: arith v62.
  85 *)
  86
  87 inline procedural "cic:/Coq/Arith/Le/le_pred.con" as theorem.
  88
  89 (*#* Comparison to 0 *)
  90
  91 inline procedural "cic:/Coq/Arith/Le/le_Sn_O.con" as theorem.
  92
  93 (* UNEXPORTED
  94 Hint Resolve le_Sn_O: arith v62.
  95 *)
  96
  97 inline procedural "cic:/Coq/Arith/Le/le_n_O_eq.con" as theorem.
  98
  99 (* UNEXPORTED
 100 Hint Immediate le_n_O_eq: arith v62.
 101 *)
 102
 103 (*#* Negative properties *)
 104
 105 inline procedural "cic:/Coq/Arith/Le/le_Sn_n.con" as theorem.
 106
 107 (* UNEXPORTED
 108 Hint Resolve le_Sn_n: arith v62.
 109 *)
 110
 111 (*#* Antisymmetry *)
 112
 113 inline procedural "cic:/Coq/Arith/Le/le_antisym.con" as theorem.
 114
 115 (* UNEXPORTED
 116 Hint Immediate le_antisym: arith v62.
 117 *)
 118
 119 (*#* A different elimination principle for the order on natural numbers *)
 120
 121 inline procedural "cic:/Coq/Arith/Le/le_elim_rel.con" as lemma.
 122