1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (* $Id: Zbool.v,v 1.4.2.1 2004/07/16 19:31:21 herbelin Exp $ *)
35 include "ZArith/BinInt.ma".
37 include "ZArith/Zeven.ma".
39 include "ZArith/Zorder.ma".
41 include "ZArith/Zcompare.ma".
43 include "ZArith/ZArith_dec.ma".
45 include "Bool/Sumbool.ma".
47 (*#* The decidability of equality and order relations over
48 type [Z] give some boolean functions with the adequate specification. *)
50 inline procedural "cic:/Coq/ZArith/Zbool/Z_lt_ge_bool.con" as definition.
52 inline procedural "cic:/Coq/ZArith/Zbool/Z_ge_lt_bool.con" as definition.
54 inline procedural "cic:/Coq/ZArith/Zbool/Z_le_gt_bool.con" as definition.
56 inline procedural "cic:/Coq/ZArith/Zbool/Z_gt_le_bool.con" as definition.
58 inline procedural "cic:/Coq/ZArith/Zbool/Z_eq_bool.con" as definition.
60 inline procedural "cic:/Coq/ZArith/Zbool/Z_noteq_bool.con" as definition.
62 inline procedural "cic:/Coq/ZArith/Zbool/Zeven_odd_bool.con" as definition.
64 (*#*********************************************************************)
66 (*#* Boolean comparisons of binary integers *)
68 inline procedural "cic:/Coq/ZArith/Zbool/Zle_bool.con" as definition.
70 inline procedural "cic:/Coq/ZArith/Zbool/Zge_bool.con" as definition.
72 inline procedural "cic:/Coq/ZArith/Zbool/Zlt_bool.con" as definition.
74 inline procedural "cic:/Coq/ZArith/Zbool/Zgt_bool.con" as definition.
76 inline procedural "cic:/Coq/ZArith/Zbool/Zeq_bool.con" as definition.
78 inline procedural "cic:/Coq/ZArith/Zbool/Zneq_bool.con" as definition.
80 inline procedural "cic:/Coq/ZArith/Zbool/Zle_cases.con" as lemma.
82 inline procedural "cic:/Coq/ZArith/Zbool/Zlt_cases.con" as lemma.
84 inline procedural "cic:/Coq/ZArith/Zbool/Zge_cases.con" as lemma.
86 inline procedural "cic:/Coq/ZArith/Zbool/Zgt_cases.con" as lemma.
88 (*#* Lemmas on [Zle_bool] used in contrib/graphs *)
90 inline procedural "cic:/Coq/ZArith/Zbool/Zle_bool_imp_le.con" as lemma.
92 inline procedural "cic:/Coq/ZArith/Zbool/Zle_imp_le_bool.con" as lemma.
94 inline procedural "cic:/Coq/ZArith/Zbool/Zle_bool_refl.con" as lemma.
96 inline procedural "cic:/Coq/ZArith/Zbool/Zle_bool_antisym.con" as lemma.
98 inline procedural "cic:/Coq/ZArith/Zbool/Zle_bool_trans.con" as lemma.
100 inline procedural "cic:/Coq/ZArith/Zbool/Zle_bool_total.con" as definition.
102 inline procedural "cic:/Coq/ZArith/Zbool/Zle_bool_plus_mono.con" as lemma.
104 inline procedural "cic:/Coq/ZArith/Zbool/Zone_pos.con" as lemma.
106 inline procedural "cic:/Coq/ZArith/Zbool/Zone_min_pos.con" as lemma.
108 inline procedural "cic:/Coq/ZArith/Zbool/Zle_is_le_bool.con" as lemma.
110 inline procedural "cic:/Coq/ZArith/Zbool/Zge_is_le_bool.con" as lemma.
112 inline procedural "cic:/Coq/ZArith/Zbool/Zlt_is_le_bool.con" as lemma.
114 inline procedural "cic:/Coq/ZArith/Zbool/Zgt_is_le_bool.con" as lemma.