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1 (**************************************************************************)
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 (*  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 (*                              Hurkens.v                               *)
34
35 (*#***********************************************************************)
36
37 (*#* This is Hurkens paradox [Hurkens] in system U-, adapted by Herman
38     Geuvers [Geuvers] to show the inconsistency in the pure calculus of
39     constructions of a retract from Prop into a small type.
40
41     References:
42
43     - [Hurkens] A. J. Hurkens, "A simplification of Girard's paradox",
44       Proceedings of the 2nd international conference Typed Lambda-Calculi
45       and Applications (TLCA'95), 1995.
46
47     - [Geuvers] "Inconsistency of Classical Logic in Type Theory", 2001
48       (see www.cs.kun.nl/~herman/note.ps.gz).
49 *)
50
51 (* UNEXPORTED
52 Section Paradox
53 *)
54
55 (* UNEXPORTED
56 cic:/Coq/Logic/Hurkens/Paradox/bool.var
57 *)
58
59 (* UNEXPORTED
60 cic:/Coq/Logic/Hurkens/Paradox/p2b.var
61 *)
62
63 (* UNEXPORTED
64 cic:/Coq/Logic/Hurkens/Paradox/b2p.var
65 *)
66
67 (* UNEXPORTED
68 cic:/Coq/Logic/Hurkens/Paradox/p2p1.var
69 *)
70
71 (* UNEXPORTED
72 cic:/Coq/Logic/Hurkens/Paradox/p2p2.var
73 *)
74
75 (* UNEXPORTED
76 cic:/Coq/Logic/Hurkens/Paradox/B.var
77 *)
78
79 inline procedural "cic:/Coq/Logic/Hurkens/V.con" as definition.
80
81 inline procedural "cic:/Coq/Logic/Hurkens/U.con" as definition.
82
83 inline procedural "cic:/Coq/Logic/Hurkens/sb.con" as definition.
84
85 inline procedural "cic:/Coq/Logic/Hurkens/le.con" as definition.
86
87 inline procedural "cic:/Coq/Logic/Hurkens/induct.con" as definition.
88
89 inline procedural "cic:/Coq/Logic/Hurkens/WF.con" as definition.
90
91 inline procedural "cic:/Coq/Logic/Hurkens/I.con" as definition.
92
93 inline procedural "cic:/Coq/Logic/Hurkens/Omega.con" as lemma.
94
95 inline procedural "cic:/Coq/Logic/Hurkens/lemma1.con" as lemma.
96
97 inline procedural "cic:/Coq/Logic/Hurkens/lemma2.con" as lemma.
98
99 inline procedural "cic:/Coq/Logic/Hurkens/paradox.con" as theorem.
100
101 (* UNEXPORTED
102 End Paradox
103 *)
104