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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_rdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_rdeq.ma
new file mode 100644
index 000000000..f63af0dcf
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_rdeq.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rdeq_req.ma".
+include "basic_2/rt_transition/rpx_rdeq.ma".
+include "basic_2/rt_transition/rpx_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 rdeq_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_rpx … T HLK2) -HLK2 #HLK2
+elim (rdeq_rpx_trans … HLK2 … HL12) -L2 #K #H #HK2
+elim (rpx_inv_lpx_req … H) -H #K1 #HLK1 #HK1
+/3 width=5 by req_rdeq_trans, ex2_intro/
+qed-.