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

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   3 (*      ||M||                                                             *)
   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/setoids/Npossetoid".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: Npossetoid.v,v 1.3 2004/04/06 15:46:04 lcf Exp $ *)
  22
  23 include "model/setoids/Nsetoid.ma".
  24
  25 include "model/structures/Npossec.ma".
  26
  27 include "algebra/CSetoidFun.ma".
  28
  29 (*#* **Example of a setoid: [Npos]
  30
  31 *** Setoid
  32 The positive natural numbers [Npos] will be defined as a subsetoid of the
  33 natural numbers.
  34 *)
  35
  36 inline "cic:/CoRN/model/setoids/Npossetoid/Npos.con".
  37
  38 inline "cic:/CoRN/model/setoids/Npossetoid/NposP.con".
  39
  40 (*#* One and two are elements of it.
  41 *)
  42
  43 inline "cic:/CoRN/model/setoids/Npossetoid/ONEpos.con".
  44
  45 inline "cic:/CoRN/model/setoids/Npossetoid/TWOpos.con".
  46
  47 (*#* ***Addition and multiplication
  48 Because addition and multiplication preserve positivity, we can define
  49 them on this subsetoid.
  50 *)
  51
  52 inline "cic:/CoRN/model/setoids/Npossetoid/plus_resp_Npos.con".
  53
  54 inline "cic:/CoRN/model/setoids/Npossetoid/Npos_plus.con".
  55
  56 inline "cic:/CoRN/model/setoids/Npossetoid/mult_resp_Npos.con".
  57
  58 inline "cic:/CoRN/model/setoids/Npossetoid/Npos_mult.con".
  59
  60 (*#* The addition has no right unit on this set.
  61 *)
  62
  63 inline "cic:/CoRN/model/setoids/Npossetoid/no_rht_unit_Npos1.con".
  64
  65 (*#* And the multiplication doesn't have an inverse, because there can't be an
  66 inverse for 2.
  67 *)
  68
  69 inline "cic:/CoRN/model/setoids/Npossetoid/no_inverse_Nposmult1.con".
  70