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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 *)
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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".
39 Infix "{#Z}" := ap_Z (no associativity, at level 90).
42 (*#* Some properties of apartness:
45 inline "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con".
47 inline "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con".
49 inline "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con".
51 inline "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con".
53 inline "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con".
56 Some properties of the addition. [Zplus] is also defined in the standard
60 inline "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con".
62 inline "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con".
64 (*#* ***Multiplication
65 The multiplication is extensional:
68 inline "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con".
73 inline "cic:/CoRN/model/structures/Zsec/Zpos.con".
77 coercion cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2) 0 (* compounds *).
81 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
83 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
85 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
87 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
89 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
91 inline "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
93 inline "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
95 inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
97 inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
99 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".