ExtensionalFunctionRepresentative.v

Built with Alectryon, running Coq+SerAPI v8.10.0+0.7.0. Coq sources are in this panel; goals and messages will appear in the other. Bubbles () indicate interactive fragments: hover for details, tap to reveal contents. Use Ctrl+↑ Ctrl+↓ to navigate, Ctrl+🖱️ to focus.

(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

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).