(* 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                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
(*                                                                          *)
(****************************************************************************)
(*                               Conversion.v                               *)
(*                                                                          *)
(*                                Gerard Huet                               *)
(*                                                                          *)
(* Developed in V5.8  January 1993                                          *)
(* Ported    to V5.10 January 1995                                          *)
(****************************************************************************)
Inductive conv1 : lambda -> lambda -> Prop :=
| red1_conv : forall M N : lambda, red1 M N -> conv1 M N
| exp1_conv : forall M N : lambda, red1 N M -> conv1 M N.
(* Beta conversion *)
Inductive conv : lambda -> lambda -> Prop :=
| one_step_conv : forall M N : lambda, conv1 M N -> conv M N
| refl_conv : forall M : lambda, conv M M
| trans_conv : forall M N P : lambda, conv M N -> conv N P -> conv M P.

(* Specifications: *)
Lemma sym_conv : forall M N : lambda, conv M N -> conv N M.
Theorem Church_Rosser :
forall M N : lambda, conv M N -> exists P : lambda, red M P /\ red N P.