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3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
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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