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2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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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: Zeven.v,v 1.3.2.1 2004/07/16 19:31:21 herbelin Exp $ i*)
34
35 include "ZArith/BinInt.ma".
36
37 (*#*********************************************************************)
38
39 (*#* About parity: even and odd predicates on Z, division by 2 on Z *)
40
41 (*#*********************************************************************)
42
43 (*#* [Zeven], [Zodd], [Zdiv2] and their related properties *)
44
45 inline procedural "cic:/Coq/ZArith/Zeven/Zeven.con" as definition.
46
47 inline procedural "cic:/Coq/ZArith/Zeven/Zodd.con" as definition.
48
49 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_bool.con" as definition.
50
51 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_bool.con" as definition.
52
53 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_odd_dec.con" as definition.
54
55 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_dec.con" as definition.
56
57 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_dec.con" as definition.
58
59 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_not_Zodd.con" as lemma.
60
61 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_not_Zeven.con" as lemma.
62
63 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_Sn.con" as lemma.
64
65 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_Sn.con" as lemma.
66
67 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_pred.con" as lemma.
68
69 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_pred.con" as lemma.
70
71 (* UNEXPORTED
72 Hint Unfold Zeven Zodd: zarith.
73 *)
74
75 (*#*********************************************************************)
76
77 (*#* [Zdiv2] is defined on all [Z], but notice that for odd negative
78     integers it is not the euclidean quotient: in that case we have [n =
79     2*(n/2)-1] *)
80
81 inline procedural "cic:/Coq/ZArith/Zeven/Zdiv2.con" as definition.
82
83 inline procedural "cic:/Coq/ZArith/Zeven/Zeven_div2.con" as lemma.
84
85 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_div2.con" as lemma.
86
87 inline procedural "cic:/Coq/ZArith/Zeven/Zodd_div2_neg.con" as lemma.
88
89 inline procedural "cic:/Coq/ZArith/Zeven/Z_modulo_2.con" as lemma.
90
91 inline procedural "cic:/Coq/ZArith/Zeven/Zsplit2.con" as lemma.
92