--- /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/lfdeq_lfeq.ma".
+include "basic_2/rt_transition/lfpx_lfdeq.ma".
+include "basic_2/rt_transition/lfpx_lpx.ma".
+
+(* UNBOUND PARALLEL RT-TRANSITION FOR FULL LOCAL ENVIRONMENTS ***************)
+
+(* Properties with degree-based equivalence for local environments **********)
+
+(* Basic_2A1: uses: lleq_lpx_trans *)
+lemma lfdeq_lpx_trans (h) (o) (G): ∀L2,K2. ⦃G, L2⦄ ⊢ ⬈[h] K2 →
+ ∀L1. ∀T:term. L1 ≛[h, o, T] L2 →
+ ∃∃K1. ⦃G, L1⦄ ⊢ ⬈[h] K1 & K1 ≛[h, o, T] K2.
+#h #o #G #L2 #K2 #HLK2 #L1 #T #HL12
+lapply (lpx_lfpx … T HLK2) -HLK2 #HLK2
+elim (lfdeq_lfpx_trans … HLK2 … HL12) -L2 #K #H #HK2
+elim (lfpx_inv_lpx_lfeq … H) -H #K1 #HLK1 #HK1
+/3 width=5 by lfeq_lfdeq_trans, ex2_intro/
+qed-.