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diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc_fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbc_fpbs.ma
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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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/computation/fpbs_fpns.ma".
+include "basic_2/computation/fpbs_fpbs.ma".
+include "basic_2/computation/fpbc.ma".
+
+(* SINGLE-STEP "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********)
+
+(* Forward lemmas on "big tree" parallel computation for closures ***********)
+
+lemma fpbc_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄ →
+                     ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 *
+/3 width=5 by fpbu_fwd_fpbs, fpbs_trans, fpns_fpbs/
+qed-.