helm/software/matita/contribs/procedural/Coq/Sets/Ensembles.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 "Coq.ma".
  18
  19 (*#***********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  22
  23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  24
  25 (*   \VV/  **************************************************************)
  26
  27 (*    //   *      This file is distributed under the terms of the       *)
  28
  29 (*         *       GNU Lesser General Public License Version 2.1        *)
  30
  31 (*#***********************************************************************)
  32
  33 (*#***************************************************************************)
  34
  35 (*                                                                          *)
  36
  37 (*                         Naive Set Theory in Coq                          *)
  38
  39 (*                                                                          *)
  40
  41 (*                     INRIA                        INRIA                   *)
  42
  43 (*              Rocquencourt                        Sophia-Antipolis        *)
  44
  45 (*                                                                          *)
  46
  47 (*                                 Coq V6.1                                 *)
  48
  49 (*                                                                          *)
  50
  51 (*                               Gilles Kahn                                *)
  52
  53 (*                               Gerard Huet                                *)
  54
  55 (*                                                                          *)
  56
  57 (*                                                                          *)
  58
  59 (*                                                                          *)
  60
  61 (* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks  *)
  62
  63 (* to the Newton Institute for providing an exceptional work environment    *)
  64
  65 (* in Summer 1995. Several developments by E. Ledinot were an inspiration.  *)
  66
  67 (*#***************************************************************************)
  68
  69 (*i $Id: Ensembles.v,v 1.7.2.1 2004/07/16 19:31:17 herbelin Exp $ i*)
  70
  71 (* UNEXPORTED
  72 Section Ensembles
  73 *)
  74
  75 (* UNEXPORTED
  76 cic:/Coq/Sets/Ensembles/Ensembles/U.var
  77 *)
  78
  79 inline procedural "cic:/Coq/Sets/Ensembles/Ensemble.con" as definition.
  80
  81 inline procedural "cic:/Coq/Sets/Ensembles/In.con" as definition.
  82
  83 inline procedural "cic:/Coq/Sets/Ensembles/Included.con" as definition.
  84
  85 inline procedural "cic:/Coq/Sets/Ensembles/Empty_set.ind".
  86
  87 inline procedural "cic:/Coq/Sets/Ensembles/Full_set.ind".
  88
  89 (*#* NB: The following definition builds-in equality of elements in [U] as
  90    Leibniz equality.
  91
  92    This may have to be changed if we replace [U] by a Setoid on [U]
  93    with its own equality [eqs], with
  94    [In_singleton: (y: U)(eqs x y) -> (In (Singleton x) y)]. *)
  95
  96 inline procedural "cic:/Coq/Sets/Ensembles/Singleton.ind".
  97
  98 inline procedural "cic:/Coq/Sets/Ensembles/Union.ind".
  99
 100 inline procedural "cic:/Coq/Sets/Ensembles/Add.con" as definition.
 101
 102 inline procedural "cic:/Coq/Sets/Ensembles/Intersection.ind".
 103
 104 inline procedural "cic:/Coq/Sets/Ensembles/Couple.ind".
 105
 106 inline procedural "cic:/Coq/Sets/Ensembles/Triple.ind".
 107
 108 inline procedural "cic:/Coq/Sets/Ensembles/Complement.con" as definition.
 109
 110 inline procedural "cic:/Coq/Sets/Ensembles/Setminus.con" as definition.
 111
 112 inline procedural "cic:/Coq/Sets/Ensembles/Subtract.con" as definition.
 113
 114 inline procedural "cic:/Coq/Sets/Ensembles/Disjoint.ind".
 115
 116 inline procedural "cic:/Coq/Sets/Ensembles/Inhabited.ind".
 117
 118 inline procedural "cic:/Coq/Sets/Ensembles/Strict_Included.con" as definition.
 119
 120 inline procedural "cic:/Coq/Sets/Ensembles/Same_set.con" as definition.
 121
 122 (*#* Extensionality Axiom *)
 123
 124 inline procedural "cic:/Coq/Sets/Ensembles/Extensionality_Ensembles.con".
 125
 126 (* UNEXPORTED
 127 Hint Resolve Extensionality_Ensembles.
 128 *)
 129
 130 (* UNEXPORTED
 131 End Ensembles
 132 *)
 133
 134 (* UNEXPORTED
 135 Hint Unfold In Included Same_set Strict_Included Add Setminus Subtract: sets
 136   v62.
 137 *)
 138
 139 (* UNEXPORTED
 140 Hint Resolve Union_introl Union_intror Intersection_intro In_singleton
 141   Couple_l Couple_r Triple_l Triple_m Triple_r Disjoint_intro
 142   Extensionality_Ensembles: sets v62.
 143 *)
 144