helm/software/matita/contribs/procedural/Coq/Arith/Even.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 include "Init/Prelude.ma".
  20
  21 (*#***********************************************************************)
  22
  23 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  24
  25 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  26
  27 (*   \VV/  **************************************************************)
  28
  29 (*    //   *      This file is distributed under the terms of the       *)
  30
  31 (*         *       GNU Lesser General Public License Version 2.1        *)
  32
  33 (*#***********************************************************************)
  34
  35 (*i $Id: Even.v,v 1.14.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  36
  37 (*#* Here we define the predicates [even] and [odd] by mutual induction
  38     and we prove the decidability and the exclusion of those predicates.
  39     The main results about parity are proved in the module Div2. *)
  40
  41 (* UNEXPORTED
  42 Open Local Scope nat_scope.
  43 *)
  44
  45 (* UNEXPORTED
  46 Implicit Types m n : nat.
  47 *)
  48
  49 inline procedural "cic:/Coq/Arith/Even/even.ind".
  50
  51 (* UNEXPORTED
  52 Hint Constructors even: arith.
  53 *)
  54
  55 (* UNEXPORTED
  56 Hint Constructors odd: arith.
  57 *)
  58
  59 inline procedural "cic:/Coq/Arith/Even/even_or_odd.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Arith/Even/even_odd_dec.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Arith/Even/not_even_and_odd.con" as lemma.
  64
  65 inline procedural "cic:/Coq/Arith/Even/even_plus_aux.con" as lemma.
  66
  67 inline procedural "cic:/Coq/Arith/Even/even_even_plus.con" as lemma.
  68
  69 inline procedural "cic:/Coq/Arith/Even/odd_even_plus.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Arith/Even/even_plus_even_inv_r.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Arith/Even/even_plus_even_inv_l.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Arith/Even/even_plus_odd_inv_r.con" as lemma.
  76
  77 inline procedural "cic:/Coq/Arith/Even/even_plus_odd_inv_l.con" as lemma.
  78
  79 (* UNEXPORTED
  80 Hint Resolve even_even_plus odd_even_plus: arith.
  81 *)
  82
  83 inline procedural "cic:/Coq/Arith/Even/odd_plus_l.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Arith/Even/odd_plus_r.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Arith/Even/odd_plus_even_inv_l.con" as lemma.
  88
  89 inline procedural "cic:/Coq/Arith/Even/odd_plus_even_inv_r.con" as lemma.
  90
  91 inline procedural "cic:/Coq/Arith/Even/odd_plus_odd_inv_l.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Arith/Even/odd_plus_odd_inv_r.con" as lemma.
  94
  95 (* UNEXPORTED
  96 Hint Resolve odd_plus_l odd_plus_r: arith.
  97 *)
  98
  99 inline procedural "cic:/Coq/Arith/Even/even_mult_aux.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Arith/Even/even_mult_l.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Arith/Even/even_mult_r.con" as lemma.
 104
 105 (* UNEXPORTED
 106 Hint Resolve even_mult_l even_mult_r: arith.
 107 *)
 108
 109 inline procedural "cic:/Coq/Arith/Even/even_mult_inv_r.con" as lemma.
 110
 111 inline procedural "cic:/Coq/Arith/Even/even_mult_inv_l.con" as lemma.
 112
 113 inline procedural "cic:/Coq/Arith/Even/odd_mult.con" as lemma.
 114
 115 (* UNEXPORTED
 116 Hint Resolve even_mult_l even_mult_r odd_mult: arith.
 117 *)
 118
 119 inline procedural "cic:/Coq/Arith/Even/odd_mult_inv_l.con" as lemma.
 120
 121 inline procedural "cic:/Coq/Arith/Even/odd_mult_inv_r.con" as lemma.
 122