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Diffstat (limited to 'theories/Logic/ExtensionalFunctionRepresentative.v')
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diff --git a/theories/Logic/ExtensionalFunctionRepresentative.v b/theories/Logic/ExtensionalFunctionRepresentative.v new file mode 100644 index 000000000..a9da68e16 --- /dev/null +++ b/theories/Logic/ExtensionalFunctionRepresentative.v @@ -0,0 +1,24 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +(** This module states a limited form axiom of functional + extensionality which selects a canonical representative in each + class of extensional functions *) + +(** Its main interest is that it is the needed ingredient to provide + axiom of choice on setoids (a.k.a. axiom of extensional choice) + when combined with classical logic and axiom of (intensonal) + choice *) + +(** It provides extensionality of functions while still supporting (a + priori) an intensional interpretation of equality *) + +Axiom extensional_function_representative : + forall A B, exists repr, forall (f : A -> B), + (forall x, f x = repr f x) /\ + (forall g, (forall x, f x = g x) -> repr f = repr g). |