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-(***********************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
-(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
-(*   \VV/  *************************************************************)
-(*    //   *      This file is distributed under the terms of the      *)
-(*         *       GNU Lesser General Public License Version 2.1       *)
-(***********************************************************************)
-
-(* $Id$ *)
-
-Require Import DecidableType2 Morphisms RelationPairs.
-Set Implicit Arguments.
-Unset Strict Implicit.
-
-(** * Examples of Decidable Type structures. *)
-
-
-(** From two decidable types, we can build a new DecidableType
-   over their cartesian product. *)
-
-Module PairDecidableType(D1 D2:DecidableType) <: DecidableType.
-
- Definition t := (D1.t * D2.t)%type.
-
- Definition eq := (D1.eq * D2.eq)%signature.
-
- Instance eq_equiv : Equivalence eq.
-
- Definition eq_dec : forall x y, { eq x y }+{ ~eq x y }.
- Proof.
- intros (x1,x2) (y1,y2); unfold eq; simpl.
- destruct (D1.eq_dec x1 y1); destruct (D2.eq_dec x2 y2);
-  compute; intuition.
- Defined.
-
-End PairDecidableType.
-
-(** Similarly for pairs of UsualDecidableType *)
-
-Module PairUsualDecidableType(D1 D2:UsualDecidableType) <: UsualDecidableType.
- Definition t := (D1.t * D2.t)%type.
- Definition eq := @eq t.
- Program Instance eq_equiv : Equivalence eq.
- Definition eq_dec : forall x y, { eq x y }+{ ~eq x y }.
- Proof.
- intros (x1,x2) (y1,y2);
- destruct (D1.eq_dec x1 y1); destruct (D2.eq_dec x2 y2);
- unfold eq, D1.eq, D2.eq in *; simpl;
- (left; f_equal; auto; fail) ||
- (right; intro H; injection H; auto).
- Defined.
-
-End PairUsualDecidableType.