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Diffstat (limited to 'theories/Logic/ClassicalChoice.v')
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diff --git a/theories/Logic/ClassicalChoice.v b/theories/Logic/ClassicalChoice.v new file mode 100644 index 00000000..51f758e2 --- /dev/null +++ b/theories/Logic/ClassicalChoice.v @@ -0,0 +1,32 @@ +(************************************************************************) +(* 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 1.4.2.1 2004/07/16 19:31:06 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 Import ChoiceFacts. + +Theorem choice : + forall (A B:Type) (R:A -> B -> Prop), + (forall x:A, exists y : B, R x y) -> + exists f : A -> B, (forall x:A, R x (f x)). +Proof. +apply description_rel_choice_imp_funct_choice. +exact description. +exact relational_choice. +Qed.
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