helm/software/matita/contribs/procedural/Coq/Lists/List.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: List.v,v 1.9.2.1 2004/07/16 19:31:05 herbelin Exp $ i*)
  34
  35 include "Arith/Le.ma".
  36
  37 (* UNEXPORTED
  38 Section Lists
  39 *)
  40
  41 (* UNEXPORTED
  42 cic:/Coq/Lists/List/Lists/A.var
  43 *)
  44
  45 (* UNEXPORTED
  46 Set Implicit Arguments.
  47 *)
  48
  49 inline procedural "cic:/Coq/Lists/List/list.ind".
  50
  51 (* NOTATION
  52 Infix "::" := cons (at level 60, right associativity) : list_scope.
  53 *)
  54
  55 (* UNEXPORTED
  56 Open Scope list_scope.
  57 *)
  58
  59 (*#************************)
  60
  61 (*#* Discrimination       *)
  62
  63 (*#************************)
  64
  65 inline procedural "cic:/Coq/Lists/List/nil_cons.con" as lemma.
  66
  67 (*#************************)
  68
  69 (*#* Concatenation        *)
  70
  71 (*#************************)
  72
  73 inline procedural "cic:/Coq/Lists/List/app.con" as definition.
  74
  75 (* NOTATION
  76 Infix "++" := app (right associativity, at level 60) : list_scope.
  77 *)
  78
  79 inline procedural "cic:/Coq/Lists/List/app_nil_end.con" as lemma.
  80
  81 (* UNEXPORTED
  82 Hint Resolve app_nil_end.
  83 *)
  84
  85 (* UNEXPORTED
  86 Ltac now_show c := change c in |- *.
  87 *)
  88
  89 inline procedural "cic:/Coq/Lists/List/app_ass.con" as lemma.
  90
  91 (* UNEXPORTED
  92 Hint Resolve app_ass.
  93 *)
  94
  95 inline procedural "cic:/Coq/Lists/List/ass_app.con" as lemma.
  96
  97 (* UNEXPORTED
  98 Hint Resolve ass_app.
  99 *)
 100
 101 inline procedural "cic:/Coq/Lists/List/app_comm_cons.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Lists/List/app_eq_nil.con" as lemma.
 104
 105 inline procedural "cic:/Coq/Lists/List/app_cons_not_nil.con" as lemma.
 106
 107 inline procedural "cic:/Coq/Lists/List/app_eq_unit.con" as lemma.
 108
 109 inline procedural "cic:/Coq/Lists/List/app_inj_tail.con" as lemma.
 110
 111 (*#************************)
 112
 113 (*#* Head and tail        *)
 114
 115 (*#************************)
 116
 117 inline procedural "cic:/Coq/Lists/List/head.con" as definition.
 118
 119 inline procedural "cic:/Coq/Lists/List/tail.con" as definition.
 120
 121 (*#***************************************)
 122
 123 (*#* Length of lists                     *)
 124
 125 (*#***************************************)
 126
 127 inline procedural "cic:/Coq/Lists/List/length.con" as definition.
 128
 129 (*#*****************************)
 130
 131 (*#* Length order of lists     *)
 132
 133 (*#*****************************)
 134
 135 (* UNEXPORTED
 136 Section length_order
 137 *)
 138
 139 inline procedural "cic:/Coq/Lists/List/lel.con" as definition.
 140
 141 (* UNEXPORTED
 142 cic:/Coq/Lists/List/Lists/length_order/a.var
 143 *)
 144
 145 (* UNEXPORTED
 146 cic:/Coq/Lists/List/Lists/length_order/b.var
 147 *)
 148
 149 (* UNEXPORTED
 150 cic:/Coq/Lists/List/Lists/length_order/l.var
 151 *)
 152
 153 (* UNEXPORTED
 154 cic:/Coq/Lists/List/Lists/length_order/m.var
 155 *)
 156
 157 (* UNEXPORTED
 158 cic:/Coq/Lists/List/Lists/length_order/n.var
 159 *)
 160
 161 inline procedural "cic:/Coq/Lists/List/lel_refl.con" as lemma.
 162
 163 inline procedural "cic:/Coq/Lists/List/lel_trans.con" as lemma.
 164
 165 inline procedural "cic:/Coq/Lists/List/lel_cons_cons.con" as lemma.
 166
 167 inline procedural "cic:/Coq/Lists/List/lel_cons.con" as lemma.
 168
 169 inline procedural "cic:/Coq/Lists/List/lel_tail.con" as lemma.
 170
 171 inline procedural "cic:/Coq/Lists/List/lel_nil.con" as lemma.
 172
 173 (* UNEXPORTED
 174 End length_order
 175 *)
 176
 177 (* UNEXPORTED
 178 Hint Resolve lel_refl lel_cons_cons lel_cons lel_nil lel_nil nil_cons.
 179 *)
 180
 181 (*#********************************)
 182
 183 (*#* The [In] predicate           *)
 184
 185 (*#********************************)
 186
 187 inline procedural "cic:/Coq/Lists/List/In.con" as definition.
 188
 189 inline procedural "cic:/Coq/Lists/List/in_eq.con" as lemma.
 190
 191 (* UNEXPORTED
 192 Hint Resolve in_eq.
 193 *)
 194
 195 inline procedural "cic:/Coq/Lists/List/in_cons.con" as lemma.
 196
 197 (* UNEXPORTED
 198 Hint Resolve in_cons.
 199 *)
 200
 201 inline procedural "cic:/Coq/Lists/List/in_nil.con" as lemma.
 202
 203 inline procedural "cic:/Coq/Lists/List/in_inv.con" as lemma.
 204
 205 inline procedural "cic:/Coq/Lists/List/In_dec.con" as lemma.
 206
 207 inline procedural "cic:/Coq/Lists/List/in_app_or.con" as lemma.
 208
 209 (* UNEXPORTED
 210 Hint Immediate in_app_or.
 211 *)
 212
 213 inline procedural "cic:/Coq/Lists/List/in_or_app.con" as lemma.
 214
 215 (* UNEXPORTED
 216 Hint Resolve in_or_app.
 217 *)
 218
 219 (*#**************************)
 220
 221 (*#* Set inclusion on list  *)
 222
 223 (*#**************************)
 224
 225 inline procedural "cic:/Coq/Lists/List/incl.con" as definition.
 226
 227 (* UNEXPORTED
 228 Hint Unfold incl.
 229 *)
 230
 231 inline procedural "cic:/Coq/Lists/List/incl_refl.con" as lemma.
 232
 233 (* UNEXPORTED
 234 Hint Resolve incl_refl.
 235 *)
 236
 237 inline procedural "cic:/Coq/Lists/List/incl_tl.con" as lemma.
 238
 239 (* UNEXPORTED
 240 Hint Immediate incl_tl.
 241 *)
 242
 243 inline procedural "cic:/Coq/Lists/List/incl_tran.con" as lemma.
 244
 245 inline procedural "cic:/Coq/Lists/List/incl_appl.con" as lemma.
 246
 247 (* UNEXPORTED
 248 Hint Immediate incl_appl.
 249 *)
 250
 251 inline procedural "cic:/Coq/Lists/List/incl_appr.con" as lemma.
 252
 253 (* UNEXPORTED
 254 Hint Immediate incl_appr.
 255 *)
 256
 257 inline procedural "cic:/Coq/Lists/List/incl_cons.con" as lemma.
 258
 259 (* UNEXPORTED
 260 Hint Resolve incl_cons.
 261 *)
 262
 263 inline procedural "cic:/Coq/Lists/List/incl_app.con" as lemma.
 264
 265 (* UNEXPORTED
 266 Hint Resolve incl_app.
 267 *)
 268
 269 (*#*************************)
 270
 271 (*#* Nth element of a list *)
 272
 273 (*#*************************)
 274
 275 inline procedural "cic:/Coq/Lists/List/nth.con" as definition.
 276
 277 inline procedural "cic:/Coq/Lists/List/nth_ok.con" as definition.
 278
 279 inline procedural "cic:/Coq/Lists/List/nth_in_or_default.con" as lemma.
 280
 281 inline procedural "cic:/Coq/Lists/List/nth_S_cons.con" as lemma.
 282
 283 inline procedural "cic:/Coq/Lists/List/nth_error.con" as definition.
 284
 285 inline procedural "cic:/Coq/Lists/List/nth_default.con" as definition.
 286
 287 inline procedural "cic:/Coq/Lists/List/nth_In.con" as lemma.
 288
 289 (*#*******************************)
 290
 291 (*#* Decidable equality on lists *)
 292
 293 (*#*******************************)
 294
 295 inline procedural "cic:/Coq/Lists/List/list_eq_dec.con" as lemma.
 296
 297 (*#************************)
 298
 299 (*#*  Reverse             *)
 300
 301 (*#************************)
 302
 303 inline procedural "cic:/Coq/Lists/List/rev.con" as definition.
 304
 305 inline procedural "cic:/Coq/Lists/List/distr_rev.con" as lemma.
 306
 307 inline procedural "cic:/Coq/Lists/List/rev_unit.con" as remark.
 308
 309 inline procedural "cic:/Coq/Lists/List/rev_involutive.con" as lemma.
 310
 311 (*#********************************************)
 312
 313 (*#*  Reverse Induction Principle on Lists    *)
 314
 315 (*#********************************************)
 316
 317 (* UNEXPORTED
 318 Section Reverse_Induction
 319 *)
 320
 321 (* UNEXPORTED
 322 Unset Implicit Arguments.
 323 *)
 324
 325 inline procedural "cic:/Coq/Lists/List/rev_list_ind.con" as remark.
 326
 327 (* UNEXPORTED
 328 Set Implicit Arguments.
 329 *)
 330
 331 inline procedural "cic:/Coq/Lists/List/rev_ind.con" as lemma.
 332
 333 (* UNEXPORTED
 334 End Reverse_Induction
 335 *)
 336
 337 (* UNEXPORTED
 338 End Lists
 339 *)
 340
 341 (* UNEXPORTED
 342 Implicit Arguments nil [A].
 343 *)
 344
 345 (* UNEXPORTED
 346 Hint Resolve nil_cons app_nil_end ass_app app_ass: datatypes v62.
 347 *)
 348
 349 (* UNEXPORTED
 350 Hint Resolve app_comm_cons app_cons_not_nil: datatypes v62.
 351 *)
 352
 353 (* UNEXPORTED
 354 Hint Immediate app_eq_nil: datatypes v62.
 355 *)
 356
 357 (* UNEXPORTED
 358 Hint Resolve app_eq_unit app_inj_tail: datatypes v62.
 359 *)
 360
 361 (* UNEXPORTED
 362 Hint Resolve lel_refl lel_cons_cons lel_cons lel_nil lel_nil nil_cons:
 363   datatypes v62.
 364 *)
 365
 366 (* UNEXPORTED
 367 Hint Resolve in_eq in_cons in_inv in_nil in_app_or in_or_app: datatypes v62.
 368 *)
 369
 370 (* UNEXPORTED
 371 Hint Resolve incl_refl incl_tl incl_tran incl_appl incl_appr incl_cons
 372   incl_app: datatypes v62.
 373 *)
 374
 375 (* UNEXPORTED
 376 Section Functions_on_lists
 377 *)
 378
 379 (*#***************************************************************)
 380
 381 (*#* Some generic functions on lists and basic functions of them *)
 382
 383 (*#***************************************************************)
 384
 385 (* UNEXPORTED
 386 Section Map
 387 *)
 388
 389 (* UNEXPORTED
 390 cic:/Coq/Lists/List/Functions_on_lists/Map/A.var
 391 *)
 392
 393 (* UNEXPORTED
 394 cic:/Coq/Lists/List/Functions_on_lists/Map/B.var
 395 *)
 396
 397 (* UNEXPORTED
 398 cic:/Coq/Lists/List/Functions_on_lists/Map/f.var
 399 *)
 400
 401 inline procedural "cic:/Coq/Lists/List/map.con" as definition.
 402
 403 (* UNEXPORTED
 404 End Map
 405 *)
 406
 407 inline procedural "cic:/Coq/Lists/List/in_map.con" as lemma.
 408
 409 inline procedural "cic:/Coq/Lists/List/flat_map.con" as definition.
 410
 411 inline procedural "cic:/Coq/Lists/List/list_prod.con" as definition.
 412
 413 inline procedural "cic:/Coq/Lists/List/in_prod_aux.con" as lemma.
 414
 415 inline procedural "cic:/Coq/Lists/List/in_prod.con" as lemma.
 416
 417 (*#* [(list_power x y)] is [y^x], or the set of sequences of elts of [y]
 418     indexed by elts of [x], sorted in lexicographic order. *)
 419
 420 inline procedural "cic:/Coq/Lists/List/list_power.con" as definition.
 421
 422 (*#***********************************)
 423
 424 (*#* Left-to-right iterator on lists *)
 425
 426 (*#***********************************)
 427
 428 (* UNEXPORTED
 429 Section Fold_Left_Recursor
 430 *)
 431
 432 (* UNEXPORTED
 433 cic:/Coq/Lists/List/Functions_on_lists/Fold_Left_Recursor/A.var
 434 *)
 435
 436 (* UNEXPORTED
 437 cic:/Coq/Lists/List/Functions_on_lists/Fold_Left_Recursor/B.var
 438 *)
 439
 440 (* UNEXPORTED
 441 cic:/Coq/Lists/List/Functions_on_lists/Fold_Left_Recursor/f.var
 442 *)
 443
 444 inline procedural "cic:/Coq/Lists/List/fold_left.con" as definition.
 445
 446 (* UNEXPORTED
 447 End Fold_Left_Recursor
 448 *)
 449
 450 (*#***********************************)
 451
 452 (*#* Right-to-left iterator on lists *)
 453
 454 (*#***********************************)
 455
 456 (* UNEXPORTED
 457 Section Fold_Right_Recursor
 458 *)
 459
 460 (* UNEXPORTED
 461 cic:/Coq/Lists/List/Functions_on_lists/Fold_Right_Recursor/A.var
 462 *)
 463
 464 (* UNEXPORTED
 465 cic:/Coq/Lists/List/Functions_on_lists/Fold_Right_Recursor/B.var
 466 *)
 467
 468 (* UNEXPORTED
 469 cic:/Coq/Lists/List/Functions_on_lists/Fold_Right_Recursor/f.var
 470 *)
 471
 472 (* UNEXPORTED
 473 cic:/Coq/Lists/List/Functions_on_lists/Fold_Right_Recursor/a0.var
 474 *)
 475
 476 inline procedural "cic:/Coq/Lists/List/fold_right.con" as definition.
 477
 478 (* UNEXPORTED
 479 End Fold_Right_Recursor
 480 *)
 481
 482 inline procedural "cic:/Coq/Lists/List/fold_symmetric.con" as theorem.
 483
 484 (* UNEXPORTED
 485 End Functions_on_lists
 486 *)
 487
 488 (*#* Exporting list notations *)
 489
 490 (* NOTATION
 491 Infix "::" := cons (at level 60, right associativity) : list_scope.
 492 *)
 493
 494 (* NOTATION
 495 Infix "++" := app (right associativity, at level 60) : list_scope.
 496 *)
 497
 498 (* UNEXPORTED
 499 Open Scope list_scope.
 500 *)
 501
 502 (*#* Declare Scope list_scope with key list *)
 503
 504 (* UNEXPORTED
 505 Delimit Scope list_scope with list.
 506 *)
 507
 508 (* UNEXPORTED
 509 Bind Scope list_scope with list.
 510 *)
 511