helm/software/matita/contribs/procedural/Coq/ZArith/Zcompare.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.                                      *)
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  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 $$ i*)
  34
  35 include "NArith/BinPos.ma".
  36
  37 include "ZArith/BinInt.ma".
  38
  39 include "Arith/Lt.ma".
  40
  41 include "Arith/Gt.ma".
  42
  43 include "Arith/Plus.ma".
  44
  45 include "Arith/Mult.ma".
  46
  47 (* UNEXPORTED
  48 Open Local Scope Z_scope.
  49 *)
  50
  51 (*#*********************************************************************)
  52
  53 (*#* Binary Integers (Pierre Cr\233\gut, CNET, Lannion, France)            *)
  54
  55 (*#*********************************************************************)
  56
  57 (*#*********************************************************************)
  58
  59 (*#* Comparison on integers *)
  60
  61 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_refl.con" as lemma.
  62
  63 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Eq_eq.con" as lemma.
  64
  65 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Eq_iff_eq.con" as lemma.
  66
  67 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_antisym.con" as lemma.
  68
  69 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_Lt_antisym.con" as lemma.
  70
  71 (*#* Transitivity of comparison *)
  72
  73 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_trans.con" as lemma.
  74
  75 (*#* Comparison and opposite *)
  76
  77 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_opp.con" as lemma.
  78
  79 (* UNEXPORTED
  80 Hint Local Resolve Pcompare_refl.
  81 *)
  82
  83 (*#* Comparison first-order specification *)
  84
  85 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_spec.con" as lemma.
  86
  87 (*#* Comparison and addition *)
  88
  89 inline procedural "cic:/Coq/ZArith/Zcompare/weaken_Zcompare_Zplus_compatible.con" as lemma.
  90
  91 (* UNEXPORTED
  92 Hint Local Resolve ZC4.
  93 *)
  94
  95 inline procedural "cic:/Coq/ZArith/Zcompare/weak_Zcompare_Zplus_compatible.con" as lemma.
  96
  97 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_plus_compat.con" as lemma.
  98
  99 inline procedural "cic:/Coq/ZArith/Zcompare/Zplus_compare_compat.con" as lemma.
 100
 101 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_succ_Gt.con" as lemma.
 102
 103 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_Gt_not_Lt.con" as lemma.
 104
 105 (*#* Successor and comparison *)
 106
 107 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_succ_compat.con" as lemma.
 108
 109 (*#* Multiplication and comparison *)
 110
 111 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_mult_compat.con" as lemma.
 112
 113 (*#* Reverting [x ?= y] to trichotomy *)
 114
 115 inline procedural "cic:/Coq/ZArith/Zcompare/rename.con" as lemma.
 116
 117 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_elim.con" as lemma.
 118
 119 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_eq_case.con" as lemma.
 120
 121 (*#* Decompose an egality between two [?=] relations into 3 implications *)
 122
 123 inline procedural "cic:/Coq/ZArith/Zcompare/Zcompare_egal_dec.con" as lemma.
 124
 125 (*#* Relating [x ?= y] to [Zle], [Zlt], [Zge] or [Zgt] *)
 126
 127 inline procedural "cic:/Coq/ZArith/Zcompare/Zle_compare.con" as lemma.
 128
 129 inline procedural "cic:/Coq/ZArith/Zcompare/Zlt_compare.con" as lemma.
 130
 131 inline procedural "cic:/Coq/ZArith/Zcompare/Zge_compare.con" as lemma.
 132
 133 inline procedural "cic:/Coq/ZArith/Zcompare/Zgt_compare.con" as lemma.
 134
 135 (*#*********************************************************************)
 136
 137 (* Other properties *)
 138
 139 inline procedural "cic:/Coq/ZArith/Zcompare/Zmult_compare_compat_l.con" as lemma.
 140
 141 inline procedural "cic:/Coq/ZArith/Zcompare/Zmult_compare_compat_r.con" as lemma.
 142