helm/software/matita/contribs/procedural/Coq/Arith/Even.mma

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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: Even.v,v 1.14.2.1 2004/07/16 19:31:00 herbelin Exp $ i*)
  34
  35 (*#* Here we define the predicates [even] and [odd] by mutual induction
  36     and we prove the decidability and the exclusion of those predicates.
  37     The main results about parity are proved in the module Div2. *)
  38
  39 (* UNEXPORTED
  40 Open Local Scope nat_scope.
  41 *)
  42
  43 (* UNEXPORTED
  44 Implicit Types m n : nat.
  45 *)
  46
  47 inline procedural "cic:/Coq/Arith/Even/even.ind".
  48
  49 (* UNEXPORTED
  50 Hint Constructors even: arith.
  51 *)
  52
  53 (* UNEXPORTED
  54 Hint Constructors odd: arith.
  55 *)
  56
  57 inline procedural "cic:/Coq/Arith/Even/even_or_odd.con" as lemma.
  58
  59 inline procedural "cic:/Coq/Arith/Even/even_odd_dec.con" as lemma.
  60
  61 inline procedural "cic:/Coq/Arith/Even/not_even_and_odd.con" as lemma.
  62
  63 inline procedural "cic:/Coq/Arith/Even/even_plus_aux.con" as lemma.
  64
  65 inline procedural "cic:/Coq/Arith/Even/even_even_plus.con" as lemma.
  66
  67 inline procedural "cic:/Coq/Arith/Even/odd_even_plus.con" as lemma.
  68
  69 inline procedural "cic:/Coq/Arith/Even/even_plus_even_inv_r.con" as lemma.
  70
  71 inline procedural "cic:/Coq/Arith/Even/even_plus_even_inv_l.con" as lemma.
  72
  73 inline procedural "cic:/Coq/Arith/Even/even_plus_odd_inv_r.con" as lemma.
  74
  75 inline procedural "cic:/Coq/Arith/Even/even_plus_odd_inv_l.con" as lemma.
  76
  77 (* UNEXPORTED
  78 Hint Resolve even_even_plus odd_even_plus: arith.
  79 *)
  80
  81 inline procedural "cic:/Coq/Arith/Even/odd_plus_l.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Arith/Even/odd_plus_r.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Arith/Even/odd_plus_even_inv_l.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Arith/Even/odd_plus_even_inv_r.con" as lemma.
  88
  89 inline procedural "cic:/Coq/Arith/Even/odd_plus_odd_inv_l.con" as lemma.
  90
  91 inline procedural "cic:/Coq/Arith/Even/odd_plus_odd_inv_r.con" as lemma.
  92
  93 (* UNEXPORTED
  94 Hint Resolve odd_plus_l odd_plus_r: arith.
  95 *)
  96
  97 inline procedural "cic:/Coq/Arith/Even/even_mult_aux.con" as lemma.
  98
  99 inline procedural "cic:/Coq/Arith/Even/even_mult_l.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Arith/Even/even_mult_r.con" as lemma.
 102
 103 (* UNEXPORTED
 104 Hint Resolve even_mult_l even_mult_r: arith.
 105 *)
 106
 107 inline procedural "cic:/Coq/Arith/Even/even_mult_inv_r.con" as lemma.
 108
 109 inline procedural "cic:/Coq/Arith/Even/even_mult_inv_l.con" as lemma.
 110
 111 inline procedural "cic:/Coq/Arith/Even/odd_mult.con" as lemma.
 112
 113 (* UNEXPORTED
 114 Hint Resolve even_mult_l even_mult_r odd_mult: arith.
 115 *)
 116
 117 inline procedural "cic:/Coq/Arith/Even/odd_mult_inv_l.con" as lemma.
 118
 119 inline procedural "cic:/Coq/Arith/Even/odd_mult_inv_r.con" as lemma.
 120