matita/contribs/CoRN-Decl/model/structures/Zsec.ma

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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Zsec".
  18
  19 (* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
  20
  21 (*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
  22
  23 (* INCLUDE
  24 ZArith
  25 *)
  26
  27 (* INCLUDE
  28 CLogic
  29 *)
  30
  31 (*#* *[Z]
  32 ** About [Z]
  33 We consider the implementation of integers as signed binary sequences (the
  34 datatype [Z] as defined in [ZArith], in the standard library).
  35
  36 ***Apartness
  37 We define the apartness as the negation of the Leibniz equality:
  38 *)
  39
  40 inline cic:/CoRN/model/structures/Zsec/ap_Z.con.
  41
  42 (*#* Some properties of apartness:
  43 *)
  44
  45 inline cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con.
  46
  47 inline cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con.
  48
  49 inline cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con.
  50
  51 inline cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con.
  52
  53 inline cic:/CoRN/model/structures/Zsec/ONE_neq_O.con.
  54
  55 (*#* ***Addition
  56 Some properties of the addition. [Zplus] is also defined in the standard
  57 library.
  58 *)
  59
  60 inline cic:/CoRN/model/structures/Zsec/Zplus_wd0.con.
  61
  62 inline cic:/CoRN/model/structures/Zsec/Zplus_strext0.con.
  63
  64 (*#* ***Multiplication
  65 The multiplication is extensional:
  66 *)
  67
  68 inline cic:/CoRN/model/structures/Zsec/Zmult_strext0.con.
  69
  70 (*#* ***Miscellaneous
  71 *)
  72
  73 inline cic:/CoRN/model/structures/Zsec/Zpos.con.
  74
  75 (* begin hide *)
  76
  77 (* end hide *)
  78
  79 inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con.
  80
  81 inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con.
  82
  83 inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con.
  84
  85 inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con.
  86
  87 inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con.
  88
  89 inline cic:/CoRN/model/structures/Zsec/Zpos_pos.con.
  90
  91 inline cic:/CoRN/model/structures/Zsec/Zpos_neg.con.
  92
  93 inline cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con.
  94
  95 inline cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con.
  96
  97 inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con.
  98