helm/software/matita/contribs/procedural/Coq/Sets/Powerset_facts.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: Powerset_facts.v,v 1.8.2.1 2004/07/16 19:31:18 herbelin Exp $ i*)
  70
  71 include "Sets/Ensembles.ma".
  72
  73 include "Sets/Constructive_sets.ma".
  74
  75 include "Sets/Relations_1.ma".
  76
  77 include "Sets/Relations_1_facts.ma".
  78
  79 include "Sets/Partial_Order.ma".
  80
  81 include "Sets/Cpo.ma".
  82
  83 include "Sets/Powerset.ma".
  84
  85 (* UNEXPORTED
  86 Section Sets_as_an_algebra
  87 *)
  88
  89 (* UNEXPORTED
  90 cic:/Coq/Sets/Powerset_facts/Sets_as_an_algebra/U.var
  91 *)
  92
  93 (* UNEXPORTED
  94 Hint Unfold not.
  95 *)
  96
  97 inline procedural "cic:/Coq/Sets/Powerset_facts/Empty_set_zero.con" as theorem.
  98
  99 (* UNEXPORTED
 100 Hint Resolve Empty_set_zero.
 101 *)
 102
 103 inline procedural "cic:/Coq/Sets/Powerset_facts/Empty_set_zero'.con" as theorem.
 104
 105 (* UNEXPORTED
 106 Hint Resolve Empty_set_zero'.
 107 *)
 108
 109 inline procedural "cic:/Coq/Sets/Powerset_facts/less_than_empty.con" as lemma.
 110
 111 (* UNEXPORTED
 112 Hint Resolve less_than_empty.
 113 *)
 114
 115 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_commutative.con" as theorem.
 116
 117 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_associative.con" as theorem.
 118
 119 (* UNEXPORTED
 120 Hint Resolve Union_associative.
 121 *)
 122
 123 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_idempotent.con" as theorem.
 124
 125 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_absorbs.con" as lemma.
 126
 127 inline procedural "cic:/Coq/Sets/Powerset_facts/Couple_as_union.con" as theorem.
 128
 129 inline procedural "cic:/Coq/Sets/Powerset_facts/Triple_as_union.con" as theorem.
 130
 131 inline procedural "cic:/Coq/Sets/Powerset_facts/Triple_as_Couple.con" as theorem.
 132
 133 inline procedural "cic:/Coq/Sets/Powerset_facts/Triple_as_Couple_Singleton.con" as theorem.
 134
 135 inline procedural "cic:/Coq/Sets/Powerset_facts/Intersection_commutative.con" as theorem.
 136
 137 inline procedural "cic:/Coq/Sets/Powerset_facts/Distributivity.con" as theorem.
 138
 139 inline procedural "cic:/Coq/Sets/Powerset_facts/Distributivity'.con" as theorem.
 140
 141 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_add.con" as theorem.
 142
 143 (* UNEXPORTED
 144 Hint Resolve Union_add.
 145 *)
 146
 147 inline procedural "cic:/Coq/Sets/Powerset_facts/Non_disjoint_union.con" as theorem.
 148
 149 inline procedural "cic:/Coq/Sets/Powerset_facts/Non_disjoint_union'.con" as theorem.
 150
 151 inline procedural "cic:/Coq/Sets/Powerset_facts/singlx.con" as lemma.
 152
 153 (* UNEXPORTED
 154 Hint Resolve singlx.
 155 *)
 156
 157 inline procedural "cic:/Coq/Sets/Powerset_facts/incl_add.con" as lemma.
 158
 159 (* UNEXPORTED
 160 Hint Resolve incl_add.
 161 *)
 162
 163 inline procedural "cic:/Coq/Sets/Powerset_facts/incl_add_x.con" as lemma.
 164
 165 inline procedural "cic:/Coq/Sets/Powerset_facts/Add_commutative.con" as lemma.
 166
 167 inline procedural "cic:/Coq/Sets/Powerset_facts/Add_commutative'.con" as lemma.
 168
 169 inline procedural "cic:/Coq/Sets/Powerset_facts/Add_distributes.con" as lemma.
 170
 171 inline procedural "cic:/Coq/Sets/Powerset_facts/setcover_intro.con" as lemma.
 172
 173 (* UNEXPORTED
 174 Hint Resolve setcover_intro.
 175 *)
 176
 177 (* UNEXPORTED
 178 End Sets_as_an_algebra
 179 *)
 180
 181 (* UNEXPORTED
 182 Hint Resolve Empty_set_zero Empty_set_zero' Union_associative Union_add
 183   singlx incl_add: sets v62.
 184 *)
 185