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(* -*- coq-prog-args: ("-emacs-U" "-nois") -*- *)
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* Extensionality axioms that can be used when reasoning with setoids.
*
* Author: Matthieu Sozeau
* Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
* 91405 Orsay, France *)
(* $Id: SetoidAxioms.v 10739 2008-04-01 14:45:20Z herbelin $ *)
Require Import Coq.Program.Program.
Set Implicit Arguments.
Unset Strict Implicit.
Require Export Coq.Classes.SetoidClass.
(* Application of the extensionality axiom to turn a goal on leibinz equality to
a setoid equivalence. *)
Axiom setoideq_eq : forall [ sa : Setoid a ] (x y : a), x == y -> x = y.
(** Application of the extensionality principle for setoids. *)
Ltac setoid_extensionality :=
match goal with
[ |- @eq ?A ?X ?Y ] => apply (setoideq_eq (a:=A) (x:=X) (y:=Y))
end.
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