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4 (* ||A|| A project by Andrea Asperti *)
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15 (* This file was automatically generated: do not edit *********************)
19 (* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
21 (*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
23 include "algebra/CLogic.ma".
27 We consider the implementation of integers as signed binary sequences (the
28 datatype [Z] as defined in [ZArith], in the standard library).
31 We define the apartness as the negation of the Leibniz equality:
34 inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z.con".
37 Infix "{#Z}" := ap_Z (no associativity, at level 90).
40 (*#* Some properties of apartness:
43 inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con".
45 inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con".
47 inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con".
49 inline procedural "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con".
51 inline procedural "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con".
54 Some properties of the addition. [Zplus] is also defined in the standard
58 inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con".
60 inline procedural "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con".
62 (*#* ***Multiplication
63 The multiplication is extensional:
66 inline procedural "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con".
71 inline procedural "cic:/CoRN/model/structures/Zsec/Zpos.con".
76 cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2)
81 inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
83 inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
85 inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
87 inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
89 inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
91 inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
93 inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
95 inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
97 inline procedural "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
99 inline procedural "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".