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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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33 (*i $Id: ClassicalDescription.v,v 1.7.2.1 2004/07/16 19:31:06 herbelin Exp $ i*)
35 (*#* This file provides classical logic and definite description *)
37 (*#* Classical logic and definite description, as shown in [1],
38 implies the double-negation of excluded-middle in Set, hence it
39 implies a strongly classical world. Especially it conflicts with
40 impredicativity of Set, knowing that true<>false in Set.
42 [1] Laurent Chicli, Lo\239\c Pottier, Carlos Simpson, Mathematical
43 Quotients and Quotient Types in Coq, Proceedings of TYPES 2002,
44 Lecture Notes in Computer Science 2646, Springer Verlag.
47 include "Logic/Classical.ma".
49 inline procedural "cic:/Coq/Logic/ClassicalDescription/dependent_description.con".
51 (*#* Principle of definite descriptions (aka axiom of unique choice) *)
53 inline procedural "cic:/Coq/Logic/ClassicalDescription/description.con" as theorem.
55 (*#* The followig proof comes from [1] *)
57 inline procedural "cic:/Coq/Logic/ClassicalDescription/classic_set.con" as theorem.