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(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
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include "basic_2/static/lfxs_lfxs.ma".
include "basic_2/static/frees_frees.ma".

(* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)

theorem lfxs_conf: ∀R. R_confluent_lfxs R R R R →
                   ∀T. confluent … (lfxs R T).
#R #H1R #T #L0 #L1 * #f1 #Hf1 #HL01 #L2 * #f #Hf #HL02
lapply (frees_mono … Hf1 … Hf) -Hf1 #Hf12
lapply (lexs_eq_repl_back … HL01 … Hf12) -f1 #HL01
elim (lexs_conf … HL01 … HL02)