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 (*i $Id: Znat.v,v 1.3.2.1 2004/07/16 19:31:22 herbelin Exp $ i*)
35 (*#* Binary Integers (Pierre Cr\233\gut, CNET, Lannion, France) *)
37 include "Arith/Arith.ma".
39 include "NArith/BinPos.ma".
41 include "ZArith/BinInt.ma".
43 include "ZArith/Zcompare.ma".
45 include "ZArith/Zorder.ma".
47 include "Logic/Decidable.ma".
49 include "Arith/Peano_dec.ma".
51 include "Arith/Compare_dec.ma".
54 Open Local Scope Z_scope.
57 inline procedural "cic:/Coq/ZArith/Znat/neq.con" as definition.
59 (*#*********************************************************************)
61 (*#* Properties of the injection from nat into Z *)
63 inline procedural "cic:/Coq/ZArith/Znat/inj_S.con" as theorem.
65 inline procedural "cic:/Coq/ZArith/Znat/inj_plus.con" as theorem.
67 inline procedural "cic:/Coq/ZArith/Znat/inj_mult.con" as theorem.
69 inline procedural "cic:/Coq/ZArith/Znat/inj_neq.con" as theorem.
71 inline procedural "cic:/Coq/ZArith/Znat/inj_le.con" as theorem.
73 inline procedural "cic:/Coq/ZArith/Znat/inj_lt.con" as theorem.
75 inline procedural "cic:/Coq/ZArith/Znat/inj_gt.con" as theorem.
77 inline procedural "cic:/Coq/ZArith/Znat/inj_ge.con" as theorem.
79 inline procedural "cic:/Coq/ZArith/Znat/inj_eq.con" as theorem.
81 inline procedural "cic:/Coq/ZArith/Znat/intro_Z.con" as theorem.
83 inline procedural "cic:/Coq/ZArith/Znat/inj_minus1.con" as theorem.
85 inline procedural "cic:/Coq/ZArith/Znat/inj_minus2.con" as theorem.
87 inline procedural "cic:/Coq/ZArith/Znat/Zpos_eq_Z_of_nat_o_nat_of_P.con" as theorem.