helm/software/matita/contribs/procedural/Coq/Lists/ListSet.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 (*i $Id: ListSet.v,v 1.13.2.1 2004/07/16 19:31:05 herbelin Exp $ i*)
  34
  35 (*#* A Library for finite sets, implemented as lists
  36     A Library with similar interface will soon be available under
  37     the name TreeSet in the theories/Trees directory *)
  38
  39 (*#* PolyList is loaded, but not exported.
  40     This allow to "hide" the definitions, functions and theorems of PolyList
  41     and to see only the ones of ListSet *)
  42
  43 include "Lists/List.ma".
  44
  45 (* UNEXPORTED
  46 Set Implicit Arguments.
  47 *)
  48
  49 (* UNEXPORTED
  50 Section first_definitions
  51 *)
  52
  53 (* UNEXPORTED
  54 cic:/Coq/Lists/ListSet/first_definitions/A.var
  55 *)
  56
  57 (* UNEXPORTED
  58 cic:/Coq/Lists/ListSet/first_definitions/Aeq_dec.var
  59 *)
  60
  61 inline procedural "cic:/Coq/Lists/ListSet/set.con" as definition.
  62
  63 inline procedural "cic:/Coq/Lists/ListSet/empty_set.con" as definition.
  64
  65 inline procedural "cic:/Coq/Lists/ListSet/set_add.con" as definition.
  66
  67 inline procedural "cic:/Coq/Lists/ListSet/set_mem.con" as definition.
  68
  69 (*#* If [a] belongs to [x], removes [a] from [x]. If not, does nothing *)
  70
  71 inline procedural "cic:/Coq/Lists/ListSet/set_remove.con" as definition.
  72
  73 inline procedural "cic:/Coq/Lists/ListSet/set_inter.con" as definition.
  74
  75 inline procedural "cic:/Coq/Lists/ListSet/set_union.con" as definition.
  76
  77 (*#* returns the set of all els of [x] that does not belong to [y] *)
  78
  79 inline procedural "cic:/Coq/Lists/ListSet/set_diff.con" as definition.
  80
  81 inline procedural "cic:/Coq/Lists/ListSet/set_In.con" as definition.
  82
  83 inline procedural "cic:/Coq/Lists/ListSet/set_In_dec.con" as lemma.
  84
  85 inline procedural "cic:/Coq/Lists/ListSet/set_mem_ind.con" as lemma.
  86
  87 inline procedural "cic:/Coq/Lists/ListSet/set_mem_ind2.con" as lemma.
  88
  89 inline procedural "cic:/Coq/Lists/ListSet/set_mem_correct1.con" as lemma.
  90
  91 inline procedural "cic:/Coq/Lists/ListSet/set_mem_correct2.con" as lemma.
  92
  93 inline procedural "cic:/Coq/Lists/ListSet/set_mem_complete1.con" as lemma.
  94
  95 inline procedural "cic:/Coq/Lists/ListSet/set_mem_complete2.con" as lemma.
  96
  97 inline procedural "cic:/Coq/Lists/ListSet/set_add_intro1.con" as lemma.
  98
  99 inline procedural "cic:/Coq/Lists/ListSet/set_add_intro2.con" as lemma.
 100
 101 (* UNEXPORTED
 102 Hint Resolve set_add_intro1 set_add_intro2.
 103 *)
 104
 105 inline procedural "cic:/Coq/Lists/ListSet/set_add_intro.con" as lemma.
 106
 107 inline procedural "cic:/Coq/Lists/ListSet/set_add_elim.con" as lemma.
 108
 109 inline procedural "cic:/Coq/Lists/ListSet/set_add_elim2.con" as lemma.
 110
 111 (* UNEXPORTED
 112 Hint Resolve set_add_intro set_add_elim set_add_elim2.
 113 *)
 114
 115 inline procedural "cic:/Coq/Lists/ListSet/set_add_not_empty.con" as lemma.
 116
 117 inline procedural "cic:/Coq/Lists/ListSet/set_union_intro1.con" as lemma.
 118
 119 inline procedural "cic:/Coq/Lists/ListSet/set_union_intro2.con" as lemma.
 120
 121 (* UNEXPORTED
 122 Hint Resolve set_union_intro2 set_union_intro1.
 123 *)
 124
 125 inline procedural "cic:/Coq/Lists/ListSet/set_union_intro.con" as lemma.
 126
 127 inline procedural "cic:/Coq/Lists/ListSet/set_union_elim.con" as lemma.
 128
 129 inline procedural "cic:/Coq/Lists/ListSet/set_union_emptyL.con" as lemma.
 130
 131 inline procedural "cic:/Coq/Lists/ListSet/set_union_emptyR.con" as lemma.
 132
 133 inline procedural "cic:/Coq/Lists/ListSet/set_inter_intro.con" as lemma.
 134
 135 inline procedural "cic:/Coq/Lists/ListSet/set_inter_elim1.con" as lemma.
 136
 137 inline procedural "cic:/Coq/Lists/ListSet/set_inter_elim2.con" as lemma.
 138
 139 (* UNEXPORTED
 140 Hint Resolve set_inter_elim1 set_inter_elim2.
 141 *)
 142
 143 inline procedural "cic:/Coq/Lists/ListSet/set_inter_elim.con" as lemma.
 144
 145 inline procedural "cic:/Coq/Lists/ListSet/set_diff_intro.con" as lemma.
 146
 147 inline procedural "cic:/Coq/Lists/ListSet/set_diff_elim1.con" as lemma.
 148
 149 inline procedural "cic:/Coq/Lists/ListSet/set_diff_elim2.con" as lemma.
 150
 151 inline procedural "cic:/Coq/Lists/ListSet/set_diff_trivial.con" as lemma.
 152
 153 (* UNEXPORTED
 154 Hint Resolve set_diff_intro set_diff_trivial.
 155 *)
 156
 157 (* UNEXPORTED
 158 End first_definitions
 159 *)
 160
 161 (* UNEXPORTED
 162 Section other_definitions
 163 *)
 164
 165 (* UNEXPORTED
 166 cic:/Coq/Lists/ListSet/other_definitions/A.var
 167 *)
 168
 169 (* UNEXPORTED
 170 cic:/Coq/Lists/ListSet/other_definitions/B.var
 171 *)
 172
 173 inline procedural "cic:/Coq/Lists/ListSet/set_prod.con" as definition.
 174
 175 (*#* [B^A], set of applications from [A] to [B] *)
 176
 177 inline procedural "cic:/Coq/Lists/ListSet/set_power.con" as definition.
 178
 179 inline procedural "cic:/Coq/Lists/ListSet/set_map.con" as definition.
 180
 181 inline procedural "cic:/Coq/Lists/ListSet/set_fold_left.con" as definition.
 182
 183 inline procedural "cic:/Coq/Lists/ListSet/set_fold_right.con" as definition.
 184
 185 (* UNEXPORTED
 186 End other_definitions
 187 *)
 188
 189 (* UNEXPORTED
 190 Unset Implicit Arguments.
 191 *)
 192