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: Zabs.v,v 1.4.2.1 2004/07/16 19:31:21 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/Zorder.ma".
45 include "ZArith/ZArith_dec.ma".
48 Open Local Scope Z_scope.
51 (*#*********************************************************************)
53 (*#* Properties of absolute value *)
55 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_eq.con" as lemma.
57 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_non_eq.con" as lemma.
59 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_Zopp.con" as theorem.
61 (*#* Proving a property of the absolute value by cases *)
63 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_ind.con" as lemma.
65 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_intro.con" as theorem.
67 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_dec.con" as definition.
69 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_pos.con" as lemma.
71 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_eq_case.con" as theorem.
73 (*#* Triangular inequality *)
76 Hint Local Resolve Zle_neg_pos: zarith.
79 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_triangle.con" as theorem.
81 (*#* Absolute value and multiplication *)
83 inline procedural "cic:/Coq/ZArith/Zabs/Zsgn_Zabs.con" as lemma.
85 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_Zsgn.con" as lemma.
87 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_Zmult.con" as theorem.
89 (*#* absolute value in nat is compatible with order *)
91 inline procedural "cic:/Coq/ZArith/Zabs/Zabs_nat_lt.con" as lemma.