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author | Samuel Mimram <samuel.mimram@ens-lyon.org> | 2004-07-28 21:54:47 +0000 |
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committer | Samuel Mimram <samuel.mimram@ens-lyon.org> | 2004-07-28 21:54:47 +0000 |
commit | 6b649aba925b6f7462da07599fe67ebb12a3460e (patch) | |
tree | 43656bcaa51164548f3fa14e5b10de5ef1088574 /theories7/Logic/ClassicalChoice.v |
Imported Upstream version 8.0pl1upstream/8.0pl1
Diffstat (limited to 'theories7/Logic/ClassicalChoice.v')
-rw-r--r-- | theories7/Logic/ClassicalChoice.v | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/theories7/Logic/ClassicalChoice.v b/theories7/Logic/ClassicalChoice.v new file mode 100644 index 00000000..5419e958 --- /dev/null +++ b/theories7/Logic/ClassicalChoice.v @@ -0,0 +1,31 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +(*i $Id: ClassicalChoice.v,v 1.1.2.1 2004/07/16 19:31:29 herbelin Exp $ i*) + +(** This file provides classical logic and functional choice *) + +(** This file extends ClassicalDescription.v with the axiom of choice. + As ClassicalDescription.v, it implies the double-negation of + excluded-middle in Set and implies a strongly classical + world. Especially it conflicts with impredicativity of Set, knowing + that true<>false in Set. +*) + +Require Export ClassicalDescription. +Require Export RelationalChoice. +Require ChoiceFacts. + +Theorem choice : + (A:Type;B:Type;R: A->B->Prop) + ((x:A)(EX y:B|(R x y))) -> (EX f:A->B | (x:A)(R x (f x))). +Proof. +Apply description_rel_choice_imp_funct_choice. +Exact description. +Exact relational_choice. +Qed. |