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 include "Init/Prelude.ma".
  20
  21 (*#***********************************************************************)
  22
  23 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  24
  25 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  26
  27 (*   \VV/  **************************************************************)
  28
  29 (*    //   *      This file is distributed under the terms of the       *)
  30
  31 (*         *       GNU Lesser General Public License Version 2.1        *)
  32
  33 (*#***********************************************************************)
  34
  35 (*#***************************************************************************)
  36
  37 (*                                                                          *)
  38
  39 (*                         Naive Set Theory in Coq                          *)
  40
  41 (*                                                                          *)
  42
  43 (*                     INRIA                        INRIA                   *)
  44
  45 (*              Rocquencourt                        Sophia-Antipolis        *)
  46
  47 (*                                                                          *)
  48
  49 (*                                 Coq V6.1                                 *)
  50
  51 (*                                                                          *)
  52
  53 (*                               Gilles Kahn                                *)
  54
  55 (*                               Gerard Huet                                *)
  56
  57 (*                                                                          *)
  58
  59 (*                                                                          *)
  60
  61 (*                                                                          *)
  62
  63 (* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks  *)
  64
  65 (* to the Newton Institute for providing an exceptional work environment    *)
  66
  67 (* in Summer 1995. Several developments by E. Ledinot were an inspiration.  *)
  68
  69 (*#***************************************************************************)
  70
  71 (*i $Id: Ensembles.v,v 1.7.2.1 2004/07/16 19:31:17 herbelin Exp $ i*)
  72
  73 (* UNEXPORTED
  74 Section Ensembles
  75 *)
  76
  77 (* UNEXPORTED
  78 cic:/Coq/Sets/Ensembles/Ensembles/U.var
  79 *)
  80
  81 inline procedural "cic:/Coq/Sets/Ensembles/Ensemble.con" as definition.
  82
  83 inline procedural "cic:/Coq/Sets/Ensembles/In.con" as definition.
  84
  85 inline procedural "cic:/Coq/Sets/Ensembles/Included.con" as definition.
  86
  87 inline procedural "cic:/Coq/Sets/Ensembles/Empty_set.ind".
  88
  89 inline procedural "cic:/Coq/Sets/Ensembles/Full_set.ind".
  90
  91 (*#* NB: The following definition builds-in equality of elements in [U] as
  92    Leibniz equality.
  93
  94    This may have to be changed if we replace [U] by a Setoid on [U]
  95    with its own equality [eqs], with
  96    [In_singleton: (y: U)(eqs x y) -> (In (Singleton x) y)]. *)
  97
  98 inline procedural "cic:/Coq/Sets/Ensembles/Singleton.ind".
  99
 100 inline procedural "cic:/Coq/Sets/Ensembles/Union.ind".
 101
 102 inline procedural "cic:/Coq/Sets/Ensembles/Add.con" as definition.
 103
 104 inline procedural "cic:/Coq/Sets/Ensembles/Intersection.ind".
 105
 106 inline procedural "cic:/Coq/Sets/Ensembles/Couple.ind".
 107
 108 inline procedural "cic:/Coq/Sets/Ensembles/Triple.ind".
 109
 110 inline procedural "cic:/Coq/Sets/Ensembles/Complement.con" as definition.
 111
 112 inline procedural "cic:/Coq/Sets/Ensembles/Setminus.con" as definition.
 113
 114 inline procedural "cic:/Coq/Sets/Ensembles/Subtract.con" as definition.
 115
 116 inline procedural "cic:/Coq/Sets/Ensembles/Disjoint.ind".
 117
 118 inline procedural "cic:/Coq/Sets/Ensembles/Inhabited.ind".
 119
 120 inline procedural "cic:/Coq/Sets/Ensembles/Strict_Included.con" as definition.
 121
 122 inline procedural "cic:/Coq/Sets/Ensembles/Same_set.con" as definition.
 123
 124 (*#* Extensionality Axiom *)
 125
 126 inline procedural "cic:/Coq/Sets/Ensembles/Extensionality_Ensembles.con".
 127
 128 (* UNEXPORTED
 129 Hint Resolve Extensionality_Ensembles.
 130 *)
 131
 132 (* UNEXPORTED
 133 End Ensembles
 134 *)
 135
 136 (* UNEXPORTED
 137 Hint Unfold In Included Same_set Strict_Included Add Setminus Subtract: sets
 138   v62.
 139 *)
 140
 141 (* UNEXPORTED
 142 Hint Resolve Union_introl Union_intror Intersection_intro In_singleton
 143   Couple_l Couple_r Triple_l Triple_m Triple_r Disjoint_intro
 144   Extensionality_Ensembles: sets v62.
 145 *)
 146