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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_fdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_fdeq.ma
new file mode 100644
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_fdeq.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/static/fdeq.ma".
+include "basic_2/rt_computation/lpxs_rdeq.ma".
+
+(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
+
+(* Properties with degree-based equivalence on closures *********************)
+
+lemma fdeq_lpxs_trans (h) (o): ∀G1,G2,L1,L0,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L0, T2⦄ →
+                               ∀L2. ⦃G2, L0⦄ ⊢⬈*[h] L2 →
+                               ∃∃L. ⦃G1, L1⦄ ⊢⬈*[h] L & ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L0 #T1 #T2 #H1 #L2 #HL02
+elim (fdeq_inv_gen_dx … H1) -H1 #HG #HL10 #HT12 destruct
+elim (rdeq_lpxs_trans … HL02 … HL10) -L0 #L0 #HL10 #HL02
+/3 width=3 by fdeq_intro_dx, ex2_intro/
+qed-.