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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: ZArith_dec.v,v 1.11.2.1 2004/07/16 19:31:20 herbelin Exp $ i*)
35 include "Bool/Sumbool.ma".
37 include "ZArith/BinInt.ma".
39 include "ZArith/Zorder.ma".
41 include "ZArith/Zcompare.ma".
44 Open Local Scope Z_scope.
47 inline procedural "cic:/Coq/ZArith/ZArith_dec/Dcompare_inf.con" as lemma.
49 inline procedural "cic:/Coq/ZArith/ZArith_dec/Zcompare_rec.con" as lemma.
56 cic:/Coq/ZArith/ZArith_dec/decidability/x.var
60 cic:/Coq/ZArith/ZArith_dec/decidability/y.var
63 (*#* Decidability of equality on binary integers *)
65 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_eq_dec.con" as definition.
67 (*#* Decidability of order on binary integers *)
69 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_lt_dec.con" as definition.
71 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_le_dec.con" as definition.
73 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_gt_dec.con" as definition.
75 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_ge_dec.con" as definition.
77 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_lt_ge_dec.con" as definition.
79 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_lt_le_dec.con" as lemma.
81 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_le_gt_dec.con" as definition.
83 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_gt_le_dec.con" as definition.
85 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_ge_lt_dec.con" as definition.
87 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_le_lt_eq_dec.con" as definition.
93 (*#* Cotransitivity of order on binary integers *)
95 inline procedural "cic:/Coq/ZArith/ZArith_dec/Zlt_cotrans.con" as lemma.
97 inline procedural "cic:/Coq/ZArith/ZArith_dec/Zlt_cotrans_pos.con" as lemma.
99 inline procedural "cic:/Coq/ZArith/ZArith_dec/Zlt_cotrans_neg.con" as lemma.
101 inline procedural "cic:/Coq/ZArith/ZArith_dec/not_Zeq_inf.con" as lemma.
103 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_dec.con" as lemma.
105 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_dec'.con" as lemma.
107 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_zerop.con" as definition.
109 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_notzerop.con" as definition.
111 inline procedural "cic:/Coq/ZArith/ZArith_dec/Z_noteq_dec.con" as definition.