(* This program is free software; you can redistribute it and/or      *)
(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
(* of the License, or (at your option) any later version.             *)
(*                                                                    *)
(* This program is distributed in the hope that it will be useful,    *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of     *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
(*                                                                    *)
(* You should have received a copy of the GNU Lesser General Public   *)
(* License along with this program; if not, write to the Free         *)
(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
Set Implicit Arguments.
Unset Strict Implicit.
Require Export Sets.
(** Title "Cartesian product of two sets." *)
Section Def.
Variable E F : Setoid.
Comments "The type of elements of a cartesian product:".
Record cart_type : Type :=  {cart_l : E; cart_r : F}.
Comments "Equality of couples:".
Definition cart_eq (x y : cart_type) :=
Equal (cart_l x) (cart_l y) /\ Equal (cart_r x) (cart_r y).

Lemma cart_eq_equiv : equivalence cart_eq.
red in |- *.