helm/software/matita/contribs/procedural/Coq/ZArith/Zcomplements.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: Zcomplements.v,v 1.26.2.1 2004/07/16 19:31:21 herbelin Exp $ i*)
  34
  35 include "ZArith/ZArith_base.ma".
  36
  37 include "Arith/Wf_nat.ma".
  38
  39 (* UNEXPORTED
  40 Open Local Scope Z_scope.
  41 *)
  42
  43 (*#*********************************************************************)
  44
  45 (*#* About parity *)
  46
  47 inline procedural "cic:/Coq/ZArith/Zcomplements/two_or_two_plus_one.con" as lemma.
  48
  49 (*#*********************************************************************)
  50
  51 (*#* The biggest power of 2 that is stricly less than [a]
  52
  53     Easy to compute: replace all "1" of the binary representation by
  54     "0", except the first "1" (or the first one :-) *)
  55
  56 inline procedural "cic:/Coq/ZArith/Zcomplements/floor_pos.con" as definition.
  57
  58 inline procedural "cic:/Coq/ZArith/Zcomplements/floor.con" as definition.
  59
  60 inline procedural "cic:/Coq/ZArith/Zcomplements/floor_gt0.con" as lemma.
  61
  62 inline procedural "cic:/Coq/ZArith/Zcomplements/floor_ok.con" as lemma.
  63
  64 (*#*********************************************************************)
  65
  66 (*#* Two more induction principles over [Z]. *)
  67
  68 inline procedural "cic:/Coq/ZArith/Zcomplements/Z_lt_abs_rec.con" as theorem.
  69
  70 inline procedural "cic:/Coq/ZArith/Zcomplements/Z_lt_abs_induction.con" as theorem.
  71
  72 (*#* To do case analysis over the sign of [z] *)
  73
  74 inline procedural "cic:/Coq/ZArith/Zcomplements/Zcase_sign.con" as lemma.
  75
  76 inline procedural "cic:/Coq/ZArith/Zcomplements/sqr_pos.con" as lemma.
  77
  78 (*#*********************************************************************)
  79
  80 (*#* A list length in Z, tail recursive.  *)
  81
  82 include "Lists/List.ma".
  83
  84 inline procedural "cic:/Coq/ZArith/Zcomplements/Zlength_aux.con" as definition.
  85
  86 inline procedural "cic:/Coq/ZArith/Zcomplements/Zlength.con" as definition.
  87
  88 (* UNEXPORTED
  89 Implicit Arguments Zlength [A].
  90 *)
  91
  92 (* UNEXPORTED
  93 Section Zlength_properties
  94 *)
  95
  96 (* UNEXPORTED
  97 cic:/Coq/ZArith/Zcomplements/Zlength_properties/A.var
  98 *)
  99
 100 (* UNEXPORTED
 101 Implicit Type l : list A.
 102 *)
 103
 104 inline procedural "cic:/Coq/ZArith/Zcomplements/Zlength_correct.con" as lemma.
 105
 106 inline procedural "cic:/Coq/ZArith/Zcomplements/Zlength_nil.con" as lemma.
 107
 108 inline procedural "cic:/Coq/ZArith/Zcomplements/Zlength_cons.con" as lemma.
 109
 110 inline procedural "cic:/Coq/ZArith/Zcomplements/Zlength_nil_inv.con" as lemma.
 111
 112 (* UNEXPORTED
 113 End Zlength_properties
 114 *)
 115
 116 (* UNEXPORTED
 117 Implicit Arguments Zlength_correct [A].
 118 *)
 119
 120 (* UNEXPORTED
 121 Implicit Arguments Zlength_cons [A].
 122 *)
 123
 124 (* UNEXPORTED
 125 Implicit Arguments Zlength_nil_inv [A].
 126 *)
 127