helm/software/matita/contribs/procedural/Coq/Sets/Powerset.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.v,v 1.5.2.1 2004/07/16 19:31:18 herbelin Exp $ i*)
  70
  71 include "Sets/Ensembles.ma".
  72
  73 include "Sets/Relations_1.ma".
  74
  75 include "Sets/Relations_1_facts.ma".
  76
  77 include "Sets/Partial_Order.ma".
  78
  79 include "Sets/Cpo.ma".
  80
  81 (* UNEXPORTED
  82 Section The_power_set_partial_order
  83 *)
  84
  85 (* UNEXPORTED
  86 cic:/Coq/Sets/Powerset/The_power_set_partial_order/U.var
  87 *)
  88
  89 inline procedural "cic:/Coq/Sets/Powerset/Power_set.ind".
  90
  91 (* UNEXPORTED
  92 Hint Resolve Definition_of_Power_set.
  93 *)
  94
  95 inline procedural "cic:/Coq/Sets/Powerset/Empty_set_minimal.con" as theorem.
  96
  97 (* UNEXPORTED
  98 Hint Resolve Empty_set_minimal.
  99 *)
 100
 101 inline procedural "cic:/Coq/Sets/Powerset/Power_set_Inhabited.con" as theorem.
 102
 103 (* UNEXPORTED
 104 Hint Resolve Power_set_Inhabited.
 105 *)
 106
 107 inline procedural "cic:/Coq/Sets/Powerset/Inclusion_is_an_order.con" as theorem.
 108
 109 (* UNEXPORTED
 110 Hint Resolve Inclusion_is_an_order.
 111 *)
 112
 113 inline procedural "cic:/Coq/Sets/Powerset/Inclusion_is_transitive.con" as theorem.
 114
 115 (* UNEXPORTED
 116 Hint Resolve Inclusion_is_transitive.
 117 *)
 118
 119 inline procedural "cic:/Coq/Sets/Powerset/Power_set_PO.con" as definition.
 120
 121 (* UNEXPORTED
 122 Hint Unfold Power_set_PO.
 123 *)
 124
 125 inline procedural "cic:/Coq/Sets/Powerset/Strict_Rel_is_Strict_Included.con" as theorem.
 126
 127 (* UNEXPORTED
 128 Hint Resolve Strict_Rel_Transitive Strict_Rel_is_Strict_Included.
 129 *)
 130
 131 inline procedural "cic:/Coq/Sets/Powerset/Strict_inclusion_is_transitive_with_inclusion.con" as lemma.
 132
 133 inline procedural "cic:/Coq/Sets/Powerset/Strict_inclusion_is_transitive_with_inclusion_left.con" as lemma.
 134
 135 inline procedural "cic:/Coq/Sets/Powerset/Strict_inclusion_is_transitive.con" as lemma.
 136
 137 inline procedural "cic:/Coq/Sets/Powerset/Empty_set_is_Bottom.con" as theorem.
 138
 139 (* UNEXPORTED
 140 Hint Resolve Empty_set_is_Bottom.
 141 *)
 142
 143 inline procedural "cic:/Coq/Sets/Powerset/Union_minimal.con" as theorem.
 144
 145 (* UNEXPORTED
 146 Hint Resolve Union_minimal.
 147 *)
 148
 149 inline procedural "cic:/Coq/Sets/Powerset/Intersection_maximal.con" as theorem.
 150
 151 inline procedural "cic:/Coq/Sets/Powerset/Union_increases_l.con" as theorem.
 152
 153 inline procedural "cic:/Coq/Sets/Powerset/Union_increases_r.con" as theorem.
 154
 155 inline procedural "cic:/Coq/Sets/Powerset/Intersection_decreases_l.con" as theorem.
 156
 157 inline procedural "cic:/Coq/Sets/Powerset/Intersection_decreases_r.con" as theorem.
 158
 159 (* UNEXPORTED
 160 Hint Resolve Union_increases_l Union_increases_r Intersection_decreases_l
 161   Intersection_decreases_r.
 162 *)
 163
 164 inline procedural "cic:/Coq/Sets/Powerset/Union_is_Lub.con" as theorem.
 165
 166 inline procedural "cic:/Coq/Sets/Powerset/Intersection_is_Glb.con" as theorem.
 167
 168 (* UNEXPORTED
 169 End The_power_set_partial_order
 170 *)
 171
 172 (* UNEXPORTED
 173 Hint Resolve Empty_set_minimal: sets v62.
 174 *)
 175
 176 (* UNEXPORTED
 177 Hint Resolve Power_set_Inhabited: sets v62.
 178 *)
 179
 180 (* UNEXPORTED
 181 Hint Resolve Inclusion_is_an_order: sets v62.
 182 *)
 183
 184 (* UNEXPORTED
 185 Hint Resolve Inclusion_is_transitive: sets v62.
 186 *)
 187
 188 (* UNEXPORTED
 189 Hint Resolve Union_minimal: sets v62.
 190 *)
 191
 192 (* UNEXPORTED
 193 Hint Resolve Union_increases_l: sets v62.
 194 *)
 195
 196 (* UNEXPORTED
 197 Hint Resolve Union_increases_r: sets v62.
 198 *)
 199
 200 (* UNEXPORTED
 201 Hint Resolve Intersection_decreases_l: sets v62.
 202 *)
 203
 204 (* UNEXPORTED
 205 Hint Resolve Intersection_decreases_r: sets v62.
 206 *)
 207
 208 (* UNEXPORTED
 209 Hint Resolve Empty_set_is_Bottom: sets v62.
 210 *)
 211
 212 (* UNEXPORTED
 213 Hint Resolve Strict_inclusion_is_transitive: sets v62.
 214 *)
 215