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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Nsec".
  18
  19 (* $Id: Nsec.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
  20
  21 (*#* printing {#N} $\ensuremath{\mathrel\#_{\mathbb N}}$ *)
  22
  23 (* INCLUDE
  24 Peano_dec
  25 *)
  26
  27 (* INCLUDE
  28 Relations
  29 *)
  30
  31 (* INCLUDE
  32 CLogic
  33 *)
  34
  35 (*#* *[nat]
  36 **About [nat]
  37
  38 We prove some basic lemmas of the natural numbers.
  39
  40 A variant of [0_S] from the standard library
  41 *)
  42
  43 inline cic:/CoRN/model/structures/Nsec/S_O.con.
  44
  45 (*#* ***Apartness
  46 *)
  47
  48 inline cic:/CoRN/model/structures/Nsec/ap_nat.con.
  49
  50 inline cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con.
  51
  52 inline cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con.
  53
  54 inline cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con.
  55
  56 inline cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con.
  57
  58 (*#* ***Addition
  59 *)
  60
  61 inline cic:/CoRN/model/structures/Nsec/plus_strext0.con.
  62
  63 (*#* There is no inverse for addition, because every candidate will fail for 2
  64 *)
  65
  66 inline cic:/CoRN/model/structures/Nsec/no_inverse0.con.
  67
  68 (*#* ***Multiplication
  69 *)
  70
  71 inline cic:/CoRN/model/structures/Nsec/mult_strext0.con.
  72