helm/software/matita/contribs/procedural/CoRN/model/setoids/Qsetoid.mma

   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 include "CoRN.ma".
  18
  19 (* $Id: Qsetoid.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
  20
  21 include "model/structures/Qsec.ma".
  22
  23 include "algebra/CSetoidFun.ma".
  24
  25 (*#* **Example of a setoid: [Q]
  26 ***Setoid
  27 *)
  28
  29 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_irreflexive1.con" as lemma.
  30
  31 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_symmetric1.con" as lemma.
  32
  33 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_cotransitive1.con" as lemma.
  34
  35 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_tight1.con" as lemma.
  36
  37 inline procedural "cic:/CoRN/model/setoids/Qsetoid/ap_Q_is_apartness.con" as definition.
  38
  39 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Q_as_CSetoid.con" as definition.
  40
  41 (*#* ***Addition
  42 *)
  43
  44 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_wd.con" as lemma.
  45
  46 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_strext1.con" as lemma.
  47
  48 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_bin_fun.con" as definition.
  49
  50 (*#* It is associative and commutative.
  51 *)
  52
  53 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_assoc.con" as lemma.
  54
  55 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qplus_is_commut1.con" as lemma.
  56
  57 (*#* ***Opposite
  58 *)
  59
  60 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_wd.con" as lemma.
  61
  62 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_strext.con" as lemma.
  63
  64 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qopp_is_fun.con" as definition.
  65
  66 (*#* ***Multiplication
  67 *)
  68
  69 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_wd.con" as lemma.
  70
  71 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_strext1.con" as lemma.
  72
  73 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_bin_fun.con" as definition.
  74
  75 (*#* It is associative and commutative.
  76 *)
  77
  78 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_assoc.con" as lemma.
  79
  80 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qmult_is_commut.con" as lemma.
  81
  82 (*#* ***Less-than
  83 *)
  84
  85 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_strext.con" as lemma.
  86
  87 inline procedural "cic:/CoRN/model/setoids/Qsetoid/Qlt_is_CSetoid_relation.con" as definition.
  88