helm/software/matita/contribs/CoRN-Decl/model/setoids/Npossetoid.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Npossetoid".
  18
  19 (* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *)
  20
  21 (* INCLUDE
  22 Nsetoid
  23 *)
  24
  25 (* INCLUDE
  26 Npossec
  27 *)
  28
  29 (* INCLUDE
  30 CSetoidFun
  31 *)
  32
  33 (*#* **Example of a setoid: [Npos]
  34
  35 *** Setoid
  36 The positive natural numbers [Npos] will be defined as a subsetoid of the
  37 natural numbers.
  38 *)
  39
  40 inline cic:/CoRN/model/setoids/Npossetoid/Npos.con.
  41
  42 inline cic:/CoRN/model/setoids/Npossetoid/NposP.con.
  43
  44 (*#* One and two are elements of it.
  45 *)
  46
  47 inline cic:/CoRN/model/setoids/Npossetoid/ONEpos.con.
  48
  49 inline cic:/CoRN/model/setoids/Npossetoid/TWOpos.con.
  50
  51 (*#* ***Addition and multiplication
  52 Because addition and multiplication preserve positivity, we can define
  53 them on this subsetoid.
  54 *)
  55
  56 inline cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con.
  57
  58 inline cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con.
  59
  60 inline cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con.
  61
  62 inline cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con.
  63
  64 (*#* The addition has no right unit on this set.
  65 *)
  66
  67 inline cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con.
  68
  69 (*#* And the multiplication doesn't have an inverse, because there can't be an
  70 inverse for 2.
  71 *)
  72
  73 inline cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con.
  74