helm/software/matita/contribs/procedural/Coq/Relations/Rstar.mma

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   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                             *)
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  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 include "Init/Prelude.ma".
  20
  21 (*#***********************************************************************)
  22
  23 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
  24
  25 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
  26
  27 (*   \VV/  **************************************************************)
  28
  29 (*    //   *      This file is distributed under the terms of the       *)
  30
  31 (*         *       GNU Lesser General Public License Version 2.1        *)
  32
  33 (*#***********************************************************************)
  34
  35 (*i $Id: Rstar.v,v 1.8.2.1 2004/07/16 19:31:16 herbelin Exp $ i*)
  36
  37 (*#* Properties of a binary relation [R] on type [A] *)
  38
  39 (* UNEXPORTED
  40 Section Rstar
  41 *)
  42
  43 (* UNEXPORTED
  44 cic:/Coq/Relations/Rstar/Rstar/A.var
  45 *)
  46
  47 (* UNEXPORTED
  48 cic:/Coq/Relations/Rstar/Rstar/R.var
  49 *)
  50
  51 (*#* Definition of the reflexive-transitive closure [R*] of [R] *)
  52
  53 (*#* Smallest reflexive [P] containing [R o P] *)
  54
  55 inline procedural "cic:/Coq/Relations/Rstar/Rstar.con" as definition.
  56
  57 inline procedural "cic:/Coq/Relations/Rstar/Rstar_reflexive.con" as theorem.
  58
  59 inline procedural "cic:/Coq/Relations/Rstar/Rstar_R.con" as theorem.
  60
  61 (*#* We conclude with transitivity of [Rstar] : *)
  62
  63 inline procedural "cic:/Coq/Relations/Rstar/Rstar_transitive.con" as theorem.
  64
  65 (*#* Another characterization of [R*] *)
  66
  67 (*#* Smallest reflexive [P] containing [R o R*] *)
  68
  69 inline procedural "cic:/Coq/Relations/Rstar/Rstar'.con" as definition.
  70
  71 inline procedural "cic:/Coq/Relations/Rstar/Rstar'_reflexive.con" as theorem.
  72
  73 inline procedural "cic:/Coq/Relations/Rstar/Rstar'_R.con" as theorem.
  74
  75 (*#* Equivalence of the two definitions: *)
  76
  77 inline procedural "cic:/Coq/Relations/Rstar/Rstar'_Rstar.con" as theorem.
  78
  79 inline procedural "cic:/Coq/Relations/Rstar/Rstar_Rstar'.con" as theorem.
  80
  81 (*#* Property of Commutativity of two relations *)
  82
  83 inline procedural "cic:/Coq/Relations/Rstar/commut.con" as definition.
  84
  85 (* UNEXPORTED
  86 End Rstar
  87 *)
  88