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

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   4 (*      ||A||       A project by Andrea Asperti                           *)
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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Nsec".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: Nsec.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
  22
  23 (*#* printing {#N} $\ensuremath{\mathrel\#_{\mathbb N}}$ *)
  24
  25 include "algebra/CLogic.ma".
  26
  27 (*#* *[nat]
  28 **About [nat]
  29
  30 We prove some basic lemmas of the natural numbers.
  31
  32 A variant of [0_S] from the standard library
  33 *)
  34
  35 inline "cic:/CoRN/model/structures/Nsec/S_O.con".
  36
  37 (*#* ***Apartness
  38 *)
  39
  40 inline "cic:/CoRN/model/structures/Nsec/ap_nat.con".
  41
  42 (* NOTATION
  43 Infix "{#N}" := ap_nat (no associativity, at level 90).
  44 *)
  45
  46 inline "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con".
  47
  48 inline "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con".
  49
  50 inline "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con".
  51
  52 inline "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con".
  53
  54 (*#* ***Addition
  55 *)
  56
  57 inline "cic:/CoRN/model/structures/Nsec/plus_strext0.con".
  58
  59 (*#* There is no inverse for addition, because every candidate will fail for 2
  60 *)
  61
  62 inline "cic:/CoRN/model/structures/Nsec/no_inverse0.con".
  63
  64 (*#* ***Multiplication
  65 *)
  66
  67 inline "cic:/CoRN/model/structures/Nsec/mult_strext0.con".
  68