helm/software/matita/contribs/procedural/Coq/Sets/Uniset.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: Uniset.v,v 1.9.2.1 2004/07/16 19:31:18 herbelin Exp $ i*)
  34
  35 (*#* Sets as characteristic functions *)
  36
  37 (* G. Huet 1-9-95 *)
  38
  39 (* Updated Papageno 12/98 *)
  40
  41 include "Bool/Bool.ma".
  42
  43 (* UNEXPORTED
  44 Set Implicit Arguments.
  45 *)
  46
  47 (* UNEXPORTED
  48 Section defs
  49 *)
  50
  51 (* UNEXPORTED
  52 cic:/Coq/Sets/Uniset/defs/A.var
  53 *)
  54
  55 (* UNEXPORTED
  56 cic:/Coq/Sets/Uniset/defs/eqA.var
  57 *)
  58
  59 (* UNEXPORTED
  60 cic:/Coq/Sets/Uniset/defs/eqA_dec.var
  61 *)
  62
  63 inline procedural "cic:/Coq/Sets/Uniset/uniset.ind".
  64
  65 inline procedural "cic:/Coq/Sets/Uniset/charac.con" as definition.
  66
  67 inline procedural "cic:/Coq/Sets/Uniset/Emptyset.con" as definition.
  68
  69 inline procedural "cic:/Coq/Sets/Uniset/Fullset.con" as definition.
  70
  71 inline procedural "cic:/Coq/Sets/Uniset/Singleton.con" as definition.
  72
  73 inline procedural "cic:/Coq/Sets/Uniset/In.con" as definition.
  74
  75 (* UNEXPORTED
  76 Hint Unfold In.
  77 *)
  78
  79 (*#* uniset inclusion *)
  80
  81 inline procedural "cic:/Coq/Sets/Uniset/incl.con" as definition.
  82
  83 (* UNEXPORTED
  84 Hint Unfold incl.
  85 *)
  86
  87 (*#* uniset equality *)
  88
  89 inline procedural "cic:/Coq/Sets/Uniset/seq.con" as definition.
  90
  91 (* UNEXPORTED
  92 Hint Unfold seq.
  93 *)
  94
  95 inline procedural "cic:/Coq/Sets/Uniset/leb_refl.con" as lemma.
  96
  97 (* UNEXPORTED
  98 Hint Resolve leb_refl.
  99 *)
 100
 101 inline procedural "cic:/Coq/Sets/Uniset/incl_left.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Sets/Uniset/incl_right.con" as lemma.
 104
 105 inline procedural "cic:/Coq/Sets/Uniset/seq_refl.con" as lemma.
 106
 107 (* UNEXPORTED
 108 Hint Resolve seq_refl.
 109 *)
 110
 111 inline procedural "cic:/Coq/Sets/Uniset/seq_trans.con" as lemma.
 112
 113 inline procedural "cic:/Coq/Sets/Uniset/seq_sym.con" as lemma.
 114
 115 (*#* uniset union *)
 116
 117 inline procedural "cic:/Coq/Sets/Uniset/union.con" as definition.
 118
 119 inline procedural "cic:/Coq/Sets/Uniset/union_empty_left.con" as lemma.
 120
 121 (* UNEXPORTED
 122 Hint Resolve union_empty_left.
 123 *)
 124
 125 inline procedural "cic:/Coq/Sets/Uniset/union_empty_right.con" as lemma.
 126
 127 (* UNEXPORTED
 128 Hint Resolve union_empty_right.
 129 *)
 130
 131 inline procedural "cic:/Coq/Sets/Uniset/union_comm.con" as lemma.
 132
 133 (* UNEXPORTED
 134 Hint Resolve union_comm.
 135 *)
 136
 137 inline procedural "cic:/Coq/Sets/Uniset/union_ass.con" as lemma.
 138
 139 (* UNEXPORTED
 140 Hint Resolve union_ass.
 141 *)
 142
 143 inline procedural "cic:/Coq/Sets/Uniset/seq_left.con" as lemma.
 144
 145 (* UNEXPORTED
 146 Hint Resolve seq_left.
 147 *)
 148
 149 inline procedural "cic:/Coq/Sets/Uniset/seq_right.con" as lemma.
 150
 151 (* UNEXPORTED
 152 Hint Resolve seq_right.
 153 *)
 154
 155 (*#* All the proofs that follow duplicate [Multiset_of_A] *)
 156
 157 (*#* Here we should make uniset an abstract datatype, by hiding [Charac],
 158     [union], [charac]; all further properties are proved abstractly *)
 159
 160 include "Sets/Permut.ma".
 161
 162 inline procedural "cic:/Coq/Sets/Uniset/union_rotate.con" as lemma.
 163
 164 inline procedural "cic:/Coq/Sets/Uniset/seq_congr.con" as lemma.
 165
 166 inline procedural "cic:/Coq/Sets/Uniset/union_perm_left.con" as lemma.
 167
 168 inline procedural "cic:/Coq/Sets/Uniset/uniset_twist1.con" as lemma.
 169
 170 inline procedural "cic:/Coq/Sets/Uniset/uniset_twist2.con" as lemma.
 171
 172 (*#* specific for treesort *)
 173
 174 inline procedural "cic:/Coq/Sets/Uniset/treesort_twist1.con" as lemma.
 175
 176 inline procedural "cic:/Coq/Sets/Uniset/treesort_twist2.con" as lemma.
 177
 178 (*i theory of minter to do similarly
 179 Require Min.
 180 (* uniset intersection *)
 181 Definition minter := [m1,m2:uniset]
 182     (Charac [a:A](andb (charac m1 a)(charac m2 a))).
 183 i*)
 184
 185 (* UNEXPORTED
 186 End defs
 187 *)
 188
 189 (* UNEXPORTED
 190 Unset Implicit Arguments.
 191 *)
 192