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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 *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Zsec".
21 (* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
23 (*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
25 include "algebra/CLogic.ma".
29 We consider the implementation of integers as signed binary sequences (the
30 datatype [Z] as defined in [ZArith], in the standard library).
33 We define the apartness as the negation of the Leibniz equality:
36 inline "cic:/CoRN/model/structures/Zsec/ap_Z.con".
38 (*#* Some properties of apartness:
41 inline "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con".
43 inline "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con".
45 inline "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con".
47 inline "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con".
49 inline "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con".
52 Some properties of the addition. [Zplus] is also defined in the standard
56 inline "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con".
58 inline "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con".
60 (*#* ***Multiplication
61 The multiplication is extensional:
64 inline "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con".
69 inline "cic:/CoRN/model/structures/Zsec/Zpos.con".
73 coercion "cic:/matita/CoRN-Decl/model/structures/Zsec/Zpos.con" 0 (* compounds *).
77 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
79 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
81 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
83 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
85 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
87 inline "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
89 inline "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
91 inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
93 inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
95 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".