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(************************************************************************)
(* 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 *)
(************************************************************************)
(*i $Id$: i*)
Set Implicit Arguments.
Require Export Setoid_tac.
Require Export Setoid_Prop.
(** For backward compatibility *)
Record Setoid_Theory (A: Type) (Aeq: relation A) : Prop :=
{ Seq_refl : forall x:A, Aeq x x;
Seq_sym : forall x y:A, Aeq x y -> Aeq y x;
Seq_trans : forall x y z:A, Aeq x y -> Aeq y z -> Aeq x z }.
Implicit Arguments Setoid_Theory [].
Implicit Arguments Seq_refl [].
Implicit Arguments Seq_sym [].
Implicit Arguments Seq_trans [].
(** Some tactics for manipulating Setoid Theory not officially
declared as Setoid. *)
Ltac trans_st x := match goal with
| H : Setoid_Theory _ ?eqA |- ?eqA _ _ =>
apply (Seq_trans _ _ H) with x; auto
end.
Ltac sym_st := match goal with
| H : Setoid_Theory _ ?eqA |- ?eqA _ _ =>
apply (Seq_sym _ _ H); auto
end.
Ltac refl_st := match goal with
| H : Setoid_Theory _ ?eqA |- ?eqA _ _ =>
apply (Seq_refl _ _ H); auto
end.
Definition gen_st : forall A : Set, Setoid_Theory _ (@eq A).
Proof.
constructor; congruence.
Qed.
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