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[helm.git] / matita / contribs / CoRN-Decl / model / structures / Zsec.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Zsec".
+
+include "CoRN.ma".
+
+(* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
+
+(*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
+
+include "algebra/CLogic.ma".
+
+(*#* *[Z]
+** About [Z]
+We consider the implementation of integers as signed binary sequences (the 
+datatype [Z] as defined in [ZArith], in the standard library).
+
+***Apartness
+We define the apartness as the negation of the Leibniz equality:
+*)
+
+inline "cic:/CoRN/model/structures/Zsec/ap_Z.con".
+
+(* NOTATION
+Infix "{#Z}" := ap_Z (no associativity, at level 90).
+*)
+
+(*#* Some properties of apartness:
+*)
+
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con".
+
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con".
+
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con".
+
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con".
+
+inline "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con".
+
+(*#* ***Addition
+Some properties of the addition. [Zplus] is also defined in the standard 
+library.
+*)
+
+inline "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con".
+
+inline "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con".
+
+(*#* ***Multiplication
+The multiplication is extensional:
+*)
+
+inline "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con".
+
+(*#* ***Miscellaneous
+*)
+
+inline "cic:/CoRN/model/structures/Zsec/Zpos.con".
+
+(* begin hide *)
+
+coercion cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2) 0 (* compounds *).
+
+(* end hide *)
+
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
+
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
+
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
+
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
+
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
+
+inline "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
+
+inline "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
+
+inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
+
+inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
+
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".
+