(* 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                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	               Free Monoid (Kleene Closure)                          *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Monoid.
Set Implicit Arguments.
Unset Strict Implicit.
Section freem_def.
Variable A : Setoid.
Inductive Tlist : Type :=
| Empty : Tlist
| Concat1 : A -> Tlist -> Tlist.
Fixpoint Equal_Tlist (l : Tlist) : Tlist -> Prop :=
fun m : Tlist =>
match l, m with
| Empty, Empty => True
| Empty, _ => False
| Concat1 a l1, Concat1 b m1 => a =_S b /\ Equal_Tlist l1 m1
| _, _ => False
end.

(* Specifications: *)
Lemma Equal_Tlist_equiv : Equivalence Equal_Tlist.
Canonical Structure Tlist_setoid : Setoid := Equal_Tlist_equiv.