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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_ffdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_ffdeq.ma
new file mode 100644
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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/rt_transition/fpb_ffdeq.ma".
+include "basic_2/rt_computation/fsb.ma".
+
+(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
+
+(* Properties with degree-based equivalence for closures ********************)
+
+lemma fsb_ffdeq_trans: ∀h,o,G1,L1,T1. ≥[h, o] 𝐒⦃G1, L1, T1⦄ →
+                       ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ≥[h, o] 𝐒⦃G2, L2, T2⦄.
+#h #o #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1 
+#G1 #L1 #T1 #_ #IH #G2 #L2 #T2 #H12
+@fsb_intro #G #L #T #H2
+elim (ffdeq_fpb_trans … H12 … H2) -G2 -L2 -T2
+/2 width=5 by/
+qed-.