helm/software/matita/contribs/procedural/Coq/Sets/Multiset.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: Multiset.v,v 1.9.2.1 2004/07/16 19:31:17 herbelin Exp $ i*)
  34
  35 (* G. Huet 1-9-95 *)
  36
  37 include "Sets/Permut.ma".
  38
  39 (* UNEXPORTED
  40 Set Implicit Arguments.
  41 *)
  42
  43 (* UNEXPORTED
  44 Section multiset_defs
  45 *)
  46
  47 (* UNEXPORTED
  48 cic:/Coq/Sets/Multiset/multiset_defs/A.var
  49 *)
  50
  51 (* UNEXPORTED
  52 cic:/Coq/Sets/Multiset/multiset_defs/eqA.var
  53 *)
  54
  55 (* UNEXPORTED
  56 cic:/Coq/Sets/Multiset/multiset_defs/Aeq_dec.var
  57 *)
  58
  59 inline procedural "cic:/Coq/Sets/Multiset/multiset.ind".
  60
  61 inline procedural "cic:/Coq/Sets/Multiset/EmptyBag.con" as definition.
  62
  63 inline procedural "cic:/Coq/Sets/Multiset/SingletonBag.con" as definition.
  64
  65 inline procedural "cic:/Coq/Sets/Multiset/multiplicity.con" as definition.
  66
  67 (*#* multiset equality *)
  68
  69 inline procedural "cic:/Coq/Sets/Multiset/meq.con" as definition.
  70
  71 (* UNEXPORTED
  72 Hint Unfold meq multiplicity.
  73 *)
  74
  75 inline procedural "cic:/Coq/Sets/Multiset/meq_refl.con" as lemma.
  76
  77 (* UNEXPORTED
  78 Hint Resolve meq_refl.
  79 *)
  80
  81 inline procedural "cic:/Coq/Sets/Multiset/meq_trans.con" as lemma.
  82
  83 inline procedural "cic:/Coq/Sets/Multiset/meq_sym.con" as lemma.
  84
  85 (* UNEXPORTED
  86 Hint Immediate meq_sym.
  87 *)
  88
  89 (*#* multiset union *)
  90
  91 inline procedural "cic:/Coq/Sets/Multiset/munion.con" as definition.
  92
  93 inline procedural "cic:/Coq/Sets/Multiset/munion_empty_left.con" as lemma.
  94
  95 (* UNEXPORTED
  96 Hint Resolve munion_empty_left.
  97 *)
  98
  99 inline procedural "cic:/Coq/Sets/Multiset/munion_empty_right.con" as lemma.
 100
 101 include "Arith/Plus.ma".
 102
 103 (* comm. and ass. of plus *)
 104
 105 inline procedural "cic:/Coq/Sets/Multiset/munion_comm.con" as lemma.
 106
 107 (* UNEXPORTED
 108 Hint Resolve munion_comm.
 109 *)
 110
 111 inline procedural "cic:/Coq/Sets/Multiset/munion_ass.con" as lemma.
 112
 113 (* UNEXPORTED
 114 Hint Resolve munion_ass.
 115 *)
 116
 117 inline procedural "cic:/Coq/Sets/Multiset/meq_left.con" as lemma.
 118
 119 (* UNEXPORTED
 120 Hint Resolve meq_left.
 121 *)
 122
 123 inline procedural "cic:/Coq/Sets/Multiset/meq_right.con" as lemma.
 124
 125 (* UNEXPORTED
 126 Hint Resolve meq_right.
 127 *)
 128
 129 (*#* Here we should make multiset an abstract datatype, by hiding [Bag],
 130     [munion], [multiplicity]; all further properties are proved abstractly *)
 131
 132 inline procedural "cic:/Coq/Sets/Multiset/munion_rotate.con" as lemma.
 133
 134 inline procedural "cic:/Coq/Sets/Multiset/meq_congr.con" as lemma.
 135
 136 inline procedural "cic:/Coq/Sets/Multiset/munion_perm_left.con" as lemma.
 137
 138 inline procedural "cic:/Coq/Sets/Multiset/multiset_twist1.con" as lemma.
 139
 140 inline procedural "cic:/Coq/Sets/Multiset/multiset_twist2.con" as lemma.
 141
 142 (*#* specific for treesort *)
 143
 144 inline procedural "cic:/Coq/Sets/Multiset/treesort_twist1.con" as lemma.
 145
 146 inline procedural "cic:/Coq/Sets/Multiset/treesort_twist2.con" as lemma.
 147
 148 (*i theory of minter to do similarly
 149 Require Min.
 150 (* multiset intersection *)
 151 Definition minter := [m1,m2:multiset]
 152     (Bag [a:A](min (multiplicity m1 a)(multiplicity m2 a))).
 153 i*)
 154
 155 (* UNEXPORTED
 156 End multiset_defs
 157 *)
 158
 159 (* UNEXPORTED
 160 Unset Implicit Arguments.
 161 *)
 162
 163 (* UNEXPORTED
 164 Hint Unfold meq multiplicity: v62 datatypes.
 165 *)
 166
 167 (* UNEXPORTED
 168 Hint Resolve munion_empty_right munion_comm munion_ass meq_left meq_right
 169   munion_empty_left: v62 datatypes.
 170 *)
 171
 172 (* UNEXPORTED
 173 Hint Immediate meq_sym: v62 datatypes.
 174 *)
 175