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

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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 (*#***************************************************************************)
  20
  21 (*                 The Calculus of Inductive Constructions                  *)
  22
  23 (*                                                                          *)
  24
  25 (*                            Projet LogiCal                                *)
  26
  27 (*                                                                          *)
  28
  29 (*                     INRIA                        LRI-CNRS                *)
  30
  31 (*              Rocquencourt                        Orsay                   *)
  32
  33 (*                                                                          *)
  34
  35 (*                              May 29th 2002                               *)
  36
  37 (*                                                                          *)
  38
  39 (*#***************************************************************************)
  40
  41 (*                                Hurkens.v                                 *)
  42
  43 (*#***************************************************************************)
  44
  45 (*#* This is Hurkens paradox [Hurkens] in system U-, adapted by Herman
  46     Geuvers [Geuvers] to show the inconsistency in the pure calculus of
  47     constructions of a retract from Prop into a small type.
  48
  49     References:
  50
  51     - [Hurkens] A. J. Hurkens, "A simplification of Girard's paradox",
  52       Proceedings of the 2nd international conference Typed Lambda-Calculi
  53       and Applications (TLCA'95), 1995.
  54
  55     - [Geuvers] "Inconsistency of Classical Logic in Type Theory", 2001
  56       (see www.cs.kun.nl/~herman/note.ps.gz).
  57 *)
  58
  59 (* UNEXPORTED
  60 Section Paradox
  61 *)
  62
  63 (* UNEXPORTED
  64 cic:/Coq/Logic/Hurkens/Paradox/bool.var
  65 *)
  66
  67 (* UNEXPORTED
  68 cic:/Coq/Logic/Hurkens/Paradox/p2b.var
  69 *)
  70
  71 (* UNEXPORTED
  72 cic:/Coq/Logic/Hurkens/Paradox/b2p.var
  73 *)
  74
  75 (* UNEXPORTED
  76 cic:/Coq/Logic/Hurkens/Paradox/p2p1.var
  77 *)
  78
  79 (* UNEXPORTED
  80 cic:/Coq/Logic/Hurkens/Paradox/p2p2.var
  81 *)
  82
  83 (* UNEXPORTED
  84 cic:/Coq/Logic/Hurkens/Paradox/B.var
  85 *)
  86
  87 inline procedural "cic:/Coq/Logic/Hurkens/V.con" as definition.
  88
  89 inline procedural "cic:/Coq/Logic/Hurkens/U.con" as definition.
  90
  91 inline procedural "cic:/Coq/Logic/Hurkens/sb.con" as definition.
  92
  93 inline procedural "cic:/Coq/Logic/Hurkens/le.con" as definition.
  94
  95 inline procedural "cic:/Coq/Logic/Hurkens/induct.con" as definition.
  96
  97 inline procedural "cic:/Coq/Logic/Hurkens/WF.con" as definition.
  98
  99 inline procedural "cic:/Coq/Logic/Hurkens/I.con" as definition.
 100
 101 inline procedural "cic:/Coq/Logic/Hurkens/Omega.con" as lemma.
 102
 103 inline procedural "cic:/Coq/Logic/Hurkens/lemma1.con" as lemma.
 104
 105 inline procedural "cic:/Coq/Logic/Hurkens/lemma2.con" as lemma.
 106
 107 inline procedural "cic:/Coq/Logic/Hurkens/paradox.con" as theorem.
 108
 109 (* UNEXPORTED
 110 End Paradox
 111 *)
 112