Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# Library Coq.Logic.ExtensionalFunctionRepresentative

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).