helm/software/matita/contribs/procedural/Coq/Wellfounded/Lexicographic_Product.mma

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  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: Lexicographic_Product.v,v 1.12.2.1 2004/07/16 19:31:19 herbelin Exp $ i*)
  34
  35 (*#* Authors: Bruno Barras, Cristina Cornes *)
  36
  37 include "Logic/Eqdep.ma".
  38
  39 include "Relations/Relation_Operators.ma".
  40
  41 include "Wellfounded/Transitive_Closure.ma".
  42
  43 (*#*  From : Constructing Recursion Operators in Type Theory
  44      L. Paulson  JSC (1986) 2, 325-355 *)
  45
  46 (* UNEXPORTED
  47 Section WfLexicographic_Product
  48 *)
  49
  50 (* UNEXPORTED
  51 cic:/Coq/Wellfounded/Lexicographic_Product/WfLexicographic_Product/A.var
  52 *)
  53
  54 (* UNEXPORTED
  55 cic:/Coq/Wellfounded/Lexicographic_Product/WfLexicographic_Product/B.var
  56 *)
  57
  58 (* UNEXPORTED
  59 cic:/Coq/Wellfounded/Lexicographic_Product/WfLexicographic_Product/leA.var
  60 *)
  61
  62 (* UNEXPORTED
  63 cic:/Coq/Wellfounded/Lexicographic_Product/WfLexicographic_Product/leB.var
  64 *)
  65
  66 (* NOTATION
  67 Notation LexProd := (lexprod A B leA leB).
  68 *)
  69
  70 (* UNEXPORTED
  71 Hint Resolve t_step Acc_clos_trans wf_clos_trans.
  72 *)
  73
  74 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Product/acc_A_B_lexprod.con" as lemma.
  75
  76 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Product/wf_lexprod.con" as theorem.
  77
  78 (* UNEXPORTED
  79 End WfLexicographic_Product
  80 *)
  81
  82 (* UNEXPORTED
  83 Section Wf_Symmetric_Product
  84 *)
  85
  86 (* UNEXPORTED
  87 cic:/Coq/Wellfounded/Lexicographic_Product/Wf_Symmetric_Product/A.var
  88 *)
  89
  90 (* UNEXPORTED
  91 cic:/Coq/Wellfounded/Lexicographic_Product/Wf_Symmetric_Product/B.var
  92 *)
  93
  94 (* UNEXPORTED
  95 cic:/Coq/Wellfounded/Lexicographic_Product/Wf_Symmetric_Product/leA.var
  96 *)
  97
  98 (* UNEXPORTED
  99 cic:/Coq/Wellfounded/Lexicographic_Product/Wf_Symmetric_Product/leB.var
 100 *)
 101
 102 (* NOTATION
 103 Notation Symprod := (symprod A B leA leB).
 104 *)
 105
 106 (*i
 107   Local sig_prod:=
 108          [x:A*B]<{_:A&B}>Case x of [a:A][b:B](existS A [_:A]B a b) end.
 109
 110 Lemma incl_sym_lexprod: (included (A*B) Symprod
 111             (R_o_f (A*B) {_:A&B} sig_prod (lexprod A [_:A]B leA [_:A]leB))).
 112 Proof.
 113  Red.
 114  Induction x.
 115  (Induction y1;Intros).
 116  Red.
 117  Unfold sig_prod .
 118  Inversion_clear H.
 119  (Apply left_lex;Auto with sets).
 120
 121  (Apply right_lex;Auto with sets).
 122 Qed.
 123 i*)
 124
 125 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Product/Acc_symprod.con" as lemma.
 126
 127 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Product/wf_symprod.con" as lemma.
 128
 129 (* UNEXPORTED
 130 End Wf_Symmetric_Product
 131 *)
 132
 133 (* UNEXPORTED
 134 Section Swap
 135 *)
 136
 137 (* UNEXPORTED
 138 cic:/Coq/Wellfounded/Lexicographic_Product/Swap/A.var
 139 *)
 140
 141 (* UNEXPORTED
 142 cic:/Coq/Wellfounded/Lexicographic_Product/Swap/R.var
 143 *)
 144
 145 (* NOTATION
 146 Notation SwapProd := (swapprod A R).
 147 *)
 148
 149 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Product/swap_Acc.con" as lemma.
 150
 151 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Product/Acc_swapprod.con" as lemma.
 152
 153 inline procedural "cic:/Coq/Wellfounded/Lexicographic_Product/wf_swapprod.con" as lemma.
 154
 155 (* UNEXPORTED
 156 End Swap
 157 *)
 158