adamc@173: (* Copyright (c) 2008, Adam Chlipala
adamc@173:  * 
adamc@173:  * This work is licensed under a
adamc@173:  * Creative Commons Attribution-Noncommercial-No Derivative Works 3.0
adamc@173:  * Unported License.
adamc@173:  * The license text is available at:
adamc@173:  *   http://creativecommons.org/licenses/by-nc-nd/3.0/
adamc@173:  *)
adamc@173: 
adamc@173: (* Additional axioms not in the Coq standard library, including those that need impredicativity *)
adamc@173: 
adamc@173: Set Implicit Arguments.
adamc@173: 
adamc@173: Require Import Axioms.
adamc@173: Export Axioms.
adamc@173: 
adamc@173: Theorem ext_eq_forall_Set : forall (A : Type)
adamc@173:   (f g : A -> Set),
adamc@173:   (forall x, f x = g x)
adamc@173:   -> @eq Set (forall x, f x) (forall x, g x).
adamc@173:   intros.
adamc@173:   rewrite (ext_eq _ _ _ H); trivial.
adamc@173: Qed.
adamc@173: 
adamc@173: Ltac ext_eq := (apply ext_eq || apply ext_eq_Set
adamc@173:   || apply ext_eq_forall || apply ext_eq_forall_Set); intro.