helm/software/matita/contribs/procedural/Coq/Arith/Between.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: Between.v,v 1.12.2.1 2004/07/16 19:30:59 herbelin Exp $ i*)
  34
  35 include "Arith/Le.ma".
  36
  37 include "Arith/Lt.ma".
  38
  39 (* UNEXPORTED
  40 Open Local Scope nat_scope.
  41 *)
  42
  43 (* UNEXPORTED
  44 Implicit Types k l p q r : nat.
  45 *)
  46
  47 (* UNEXPORTED
  48 Section Between
  49 *)
  50
  51 (* UNEXPORTED
  52 cic:/Coq/Arith/Between/Between/P.var
  53 *)
  54
  55 (* UNEXPORTED
  56 cic:/Coq/Arith/Between/Between/Q.var
  57 *)
  58
  59 inline procedural "cic:/Coq/Arith/Between/between.ind".
  60
  61 (* UNEXPORTED
  62 Hint Constructors between: arith v62.
  63 *)
  64
  65 inline procedural "cic:/Coq/Arith/Between/bet_eq.con" as lemma.
  66
  67 (* UNEXPORTED
  68 Hint Resolve bet_eq: arith v62.
  69 *)
  70
  71 inline procedural "cic:/Coq/Arith/Between/between_le.con" as lemma.
  72
  73 (* UNEXPORTED
  74 Hint Immediate between_le: arith v62.
  75 *)
  76
  77 inline procedural "cic:/Coq/Arith/Between/between_Sk_l.con" as lemma.
  78
  79 (* UNEXPORTED
  80 Hint Resolve between_Sk_l: arith v62.
  81 *)
  82
  83 inline procedural "cic:/Coq/Arith/Between/between_restr.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Arith/Between/exists_between.ind".
  86
  87 (* UNEXPORTED
  88 Hint Constructors exists_between: arith v62.
  89 *)
  90
  91 inline procedural "cic:/Coq/Arith/Between/exists_le_S.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Arith/Between/exists_lt.con" as lemma.
  94
  95 (* UNEXPORTED
  96 Hint Immediate exists_le_S exists_lt: arith v62.
  97 *)
  98
  99 inline procedural "cic:/Coq/Arith/Between/exists_S_le.con" as lemma.
 100
 101 (* UNEXPORTED
 102 Hint Immediate exists_S_le: arith v62.
 103 *)
 104
 105 inline procedural "cic:/Coq/Arith/Between/in_int.con" as definition.
 106
 107 inline procedural "cic:/Coq/Arith/Between/in_int_intro.con" as lemma.
 108
 109 (* UNEXPORTED
 110 Hint Resolve in_int_intro: arith v62.
 111 *)
 112
 113 inline procedural "cic:/Coq/Arith/Between/in_int_lt.con" as lemma.
 114
 115 inline procedural "cic:/Coq/Arith/Between/in_int_p_Sq.con" as lemma.
 116
 117 inline procedural "cic:/Coq/Arith/Between/in_int_S.con" as lemma.
 118
 119 (* UNEXPORTED
 120 Hint Resolve in_int_S: arith v62.
 121 *)
 122
 123 inline procedural "cic:/Coq/Arith/Between/in_int_Sp_q.con" as lemma.
 124
 125 (* UNEXPORTED
 126 Hint Immediate in_int_Sp_q: arith v62.
 127 *)
 128
 129 inline procedural "cic:/Coq/Arith/Between/between_in_int.con" as lemma.
 130
 131 inline procedural "cic:/Coq/Arith/Between/in_int_between.con" as lemma.
 132
 133 inline procedural "cic:/Coq/Arith/Between/exists_in_int.con" as lemma.
 134
 135 inline procedural "cic:/Coq/Arith/Between/in_int_exists.con" as lemma.
 136
 137 inline procedural "cic:/Coq/Arith/Between/between_or_exists.con" as lemma.
 138
 139 inline procedural "cic:/Coq/Arith/Between/between_not_exists.con" as lemma.
 140
 141 inline procedural "cic:/Coq/Arith/Between/P_nth.ind".
 142
 143 inline procedural "cic:/Coq/Arith/Between/nth_le.con" as lemma.
 144
 145 inline procedural "cic:/Coq/Arith/Between/eventually.con" as definition.
 146
 147 inline procedural "cic:/Coq/Arith/Between/event_O.con" as lemma.
 148
 149 (* UNEXPORTED
 150 End Between
 151 *)
 152
 153 (* UNEXPORTED
 154 Hint Resolve nth_O bet_S bet_emp bet_eq between_Sk_l exists_S exists_le
 155   in_int_S in_int_intro: arith v62.
 156 *)
 157
 158 (* UNEXPORTED
 159 Hint Immediate in_int_Sp_q exists_le_S exists_S_le: arith v62.
 160 *)
 161