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 include "CoRN.ma".
  20
  21 (* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
  22
  23 (*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
  24
  25 include "algebra/CLogic.ma".
  26
  27 (*#* *[Z]
  28 ** About [Z]
  29 We consider the implementation of integers as signed binary sequences (the
  30 datatype [Z] as defined in [ZArith], in the standard library).
  31
  32 ***Apartness
  33 We define the apartness as the negation of the Leibniz equality:
  34 *)
  35
  36 inline "cic:/CoRN/model/structures/Zsec/ap_Z.con".
  37
  38 (* NOTATION
  39 Infix "{#Z}" := ap_Z (no associativity, at level 90).
  40 *)
  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 coercion cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2) 0 (* compounds *).
  78
  79 (* end hide *)
  80
  81 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
  82
  83 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
  84
  85 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
  86
  87 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
  88
  89 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
  90
  91 inline "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
  92
  93 inline "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
  94
  95 inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
  96
  97 inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
  98
  99 inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".
 100