--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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-.