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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                               *)
(*                                                                          *)
(****************************************************************************)
(*                               Confluence.v                               *)
(*                                                                          *)
(*                                Gerard Huet                               *)
(*                                                                          *)
(* Developed in V5.8  January 1993                                          *)
(* Ported    to V5.10 January 1995                                          *)
(****************************************************************************)
(* Confluence *)
Definition confluence (A : Set) (R : A -> A -> Prop) :=
forall x y : A,
R x y -> forall z : A, R x z -> exists u : A, R y u /\ R z u.
(* Strip lemmas *)
Definition strip :=
forall x y : lambda,
par_red x y ->
forall z : lambda,
par_red1 x z -> exists u : lambda, par_red1 y u /\ par_red z u.

Lemma lemma2 : confluence lambda par_red1 -> confluence lambda par_red.