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(* 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.

Theorem Church_Rosser :
forall M N : lambda, conv M N -> exists P : lambda, red M P /\ red N P.