helm/software/matita/contribs/procedural/Coq/Arith/Plus.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: Plus.v,v 1.18.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 (*#* Properties of addition *)
  36
  37 include "Arith/Le.ma".
  38
  39 include "Arith/Lt.ma".
  40
  41 (* UNEXPORTED
  42 Open Local Scope nat_scope.
  43 *)
  44
  45 (* UNEXPORTED
  46 Implicit Types m n p q : nat.
  47 *)
  48
  49 (*#* Zero is neutral *)
  50
  51 inline procedural "cic:/Coq/Arith/Plus/plus_0_l.con" as lemma.
  52
  53 inline procedural "cic:/Coq/Arith/Plus/plus_0_r.con" as lemma.
  54
  55 (*#* Commutativity *)
  56
  57 inline procedural "cic:/Coq/Arith/Plus/plus_comm.con" as lemma.
  58
  59 (* UNEXPORTED
  60 Hint Immediate plus_comm: arith v62.
  61 *)
  62
  63 (*#* Associativity *)
  64
  65 inline procedural "cic:/Coq/Arith/Plus/plus_Snm_nSm.con" as lemma.
  66
  67 inline procedural "cic:/Coq/Arith/Plus/plus_assoc.con" as lemma.
  68
  69 (* UNEXPORTED
  70 Hint Resolve plus_assoc: arith v62.
  71 *)
  72
  73 inline procedural "cic:/Coq/Arith/Plus/plus_permute.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Arith/Plus/plus_assoc_reverse.con" as lemma.
  76
  77 (* UNEXPORTED
  78 Hint Resolve plus_assoc_reverse: arith v62.
  79 *)
  80
  81 (*#* Simplification *)
  82
  83 inline procedural "cic:/Coq/Arith/Plus/plus_reg_l.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Arith/Plus/plus_le_reg_l.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Arith/Plus/plus_lt_reg_l.con" as lemma.
  88
  89 (*#* Compatibility with order *)
  90
  91 inline procedural "cic:/Coq/Arith/Plus/plus_le_compat_l.con" as lemma.
  92
  93 (* UNEXPORTED
  94 Hint Resolve plus_le_compat_l: arith v62.
  95 *)
  96
  97 inline procedural "cic:/Coq/Arith/Plus/plus_le_compat_r.con" as lemma.
  98
  99 (* UNEXPORTED
 100 Hint Resolve plus_le_compat_r: arith v62.
 101 *)
 102
 103 inline procedural "cic:/Coq/Arith/Plus/le_plus_l.con" as lemma.
 104
 105 (* UNEXPORTED
 106 Hint Resolve le_plus_l: arith v62.
 107 *)
 108
 109 inline procedural "cic:/Coq/Arith/Plus/le_plus_r.con" as lemma.
 110
 111 (* UNEXPORTED
 112 Hint Resolve le_plus_r: arith v62.
 113 *)
 114
 115 inline procedural "cic:/Coq/Arith/Plus/le_plus_trans.con" as theorem.
 116
 117 (* UNEXPORTED
 118 Hint Resolve le_plus_trans: arith v62.
 119 *)
 120
 121 inline procedural "cic:/Coq/Arith/Plus/lt_plus_trans.con" as theorem.
 122
 123 (* UNEXPORTED
 124 Hint Immediate lt_plus_trans: arith v62.
 125 *)
 126
 127 inline procedural "cic:/Coq/Arith/Plus/plus_lt_compat_l.con" as lemma.
 128
 129 (* UNEXPORTED
 130 Hint Resolve plus_lt_compat_l: arith v62.
 131 *)
 132
 133 inline procedural "cic:/Coq/Arith/Plus/plus_lt_compat_r.con" as lemma.
 134
 135 (* UNEXPORTED
 136 Hint Resolve plus_lt_compat_r: arith v62.
 137 *)
 138
 139 inline procedural "cic:/Coq/Arith/Plus/plus_le_compat.con" as lemma.
 140
 141 inline procedural "cic:/Coq/Arith/Plus/plus_le_lt_compat.con" as lemma.
 142
 143 inline procedural "cic:/Coq/Arith/Plus/plus_lt_le_compat.con" as lemma.
 144
 145 inline procedural "cic:/Coq/Arith/Plus/plus_lt_compat.con" as lemma.
 146
 147 (*#* Inversion lemmas *)
 148
 149 inline procedural "cic:/Coq/Arith/Plus/plus_is_O.con" as lemma.
 150
 151 inline procedural "cic:/Coq/Arith/Plus/plus_is_one.con" as definition.
 152
 153 (*#* Derived properties *)
 154
 155 inline procedural "cic:/Coq/Arith/Plus/plus_permute_2_in_4.con" as lemma.
 156
 157 (*#* Tail-recursive plus *)
 158
 159 (*#* [tail_plus] is an alternative definition for [plus] which is
 160     tail-recursive, whereas [plus] is not. This can be useful
 161     when extracting programs. *)
 162
 163 inline procedural "cic:/Coq/Arith/Plus/plus_acc.con" as definition.
 164
 165 inline procedural "cic:/Coq/Arith/Plus/tail_plus.con" as definition.
 166
 167 inline procedural "cic:/Coq/Arith/Plus/plus_tail_plus.con" as lemma.
 168