helm/software/matita/contribs/procedural/Coq/Logic/Hurkens.mma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  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 (*                              Hurkens.v                               *)
  36
  37 (*#***********************************************************************)
  38
  39 (*#* This is Hurkens paradox [Hurkens] in system U-, adapted by Herman
  40     Geuvers [Geuvers] to show the inconsistency in the pure calculus of
  41     constructions of a retract from Prop into a small type.
  42
  43     References:
  44
  45     - [Hurkens] A. J. Hurkens, "A simplification of Girard's paradox",
  46       Proceedings of the 2nd international conference Typed Lambda-Calculi
  47       and Applications (TLCA'95), 1995.
  48
  49     - [Geuvers] "Inconsistency of Classical Logic in Type Theory", 2001
  50       (see www.cs.kun.nl/~herman/note.ps.gz).
  51 *)
  52
  53 (* UNEXPORTED
  54 Section Paradox
  55 *)
  56
  57 (* UNEXPORTED
  58 cic:/Coq/Logic/Hurkens/Paradox/bool.var
  59 *)
  60
  61 (* UNEXPORTED
  62 cic:/Coq/Logic/Hurkens/Paradox/p2b.var
  63 *)
  64
  65 (* UNEXPORTED
  66 cic:/Coq/Logic/Hurkens/Paradox/b2p.var
  67 *)
  68
  69 (* UNEXPORTED
  70 cic:/Coq/Logic/Hurkens/Paradox/p2p1.var
  71 *)
  72
  73 (* UNEXPORTED
  74 cic:/Coq/Logic/Hurkens/Paradox/p2p2.var
  75 *)
  76
  77 (* UNEXPORTED
  78 cic:/Coq/Logic/Hurkens/Paradox/B.var
  79 *)
  80
  81 inline procedural "cic:/Coq/Logic/Hurkens/V.con" as definition.
  82
  83 inline procedural "cic:/Coq/Logic/Hurkens/U.con" as definition.
  84
  85 inline procedural "cic:/Coq/Logic/Hurkens/sb.con" as definition.
  86
  87 inline procedural "cic:/Coq/Logic/Hurkens/le.con" as definition.
  88
  89 inline procedural "cic:/Coq/Logic/Hurkens/induct.con" as definition.
  90
  91 inline procedural "cic:/Coq/Logic/Hurkens/WF.con" as definition.
  92
  93 inline procedural "cic:/Coq/Logic/Hurkens/I.con" as definition.
  94
  95 inline procedural "cic:/Coq/Logic/Hurkens/Omega.con" as lemma.
  96
  97 inline procedural "cic:/Coq/Logic/Hurkens/lemma1.con" as lemma.
  98
  99 inline procedural "cic:/Coq/Logic/Hurkens/lemma2.con" as lemma.
 100
 101 inline procedural "cic:/Coq/Logic/Hurkens/paradox.con" as theorem.
 102
 103 (* UNEXPORTED
 104 End Paradox
 105 *)
 106