Adding a file providing extensional choice (i.e. choice over setoids).

Also integrating suggestions from Théo.

1 files changed, 24 insertions, 0 deletions

diff --git a/theories/Logic/ExtensionalFunctionRepresentative.v b/theories/Logic/ExtensionalFunctionRepresentative.v
new file mode 100644
index 000000000..a9da68e16
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+++ b/theories/Logic/ExtensionalFunctionRepresentative.v
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+(************************************************************************)
+(*  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).