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21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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35 (*#***********************************************************************)
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.
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.
47 - [Geuvers] "Inconsistency of Classical Logic in Type Theory", 2001
48 (see www.cs.kun.nl/~herman/note.ps.gz).
56 cic:/Coq/Logic/Hurkens/Paradox/bool.var
60 cic:/Coq/Logic/Hurkens/Paradox/p2b.var
64 cic:/Coq/Logic/Hurkens/Paradox/b2p.var
68 cic:/Coq/Logic/Hurkens/Paradox/p2p1.var
72 cic:/Coq/Logic/Hurkens/Paradox/p2p2.var
76 cic:/Coq/Logic/Hurkens/Paradox/B.var
79 inline procedural "cic:/Coq/Logic/Hurkens/V.con" as definition.
81 inline procedural "cic:/Coq/Logic/Hurkens/U.con" as definition.
83 inline procedural "cic:/Coq/Logic/Hurkens/sb.con" as definition.
85 inline procedural "cic:/Coq/Logic/Hurkens/le.con" as definition.
87 inline procedural "cic:/Coq/Logic/Hurkens/induct.con" as definition.
89 inline procedural "cic:/Coq/Logic/Hurkens/WF.con" as definition.
91 inline procedural "cic:/Coq/Logic/Hurkens/I.con" as definition.
93 inline procedural "cic:/Coq/Logic/Hurkens/Omega.con" as lemma.
95 inline procedural "cic:/Coq/Logic/Hurkens/lemma1.con" as lemma.
97 inline procedural "cic:/Coq/Logic/Hurkens/lemma2.con" as lemma.
99 inline procedural "cic:/Coq/Logic/Hurkens/paradox.con" as theorem.