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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fdeq.ma
new file mode 100644
index 000000000..3a86118e1
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fdeq.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/fdeq.ma".
+include "basic_2/rt_transition/cpx_rdeq.ma".
+include "basic_2/rt_transition/rpx_rdeq.ma".
+
+(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
+
+(* Properties with degree-based equivalence for closures ********************)
+
+lemma fdeq_cpx_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T⦄ →
+                      ∀T2. ⦃G2, L2⦄ ⊢ T ⬈[h] T2 →
+                      ∃∃T0. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T0 & ⦃G1, L1, T0⦄ ≛[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T #H #T2 #HT2
+elim (fdeq_inv_gen_dx … H) -H #H #HL12 #HT1 destruct
+elim (rdeq_cpx_trans … HL12 … HT2) #T0 #HT0 #HT02
+lapply (cpx_rdeq_conf_dx … HT2 … HL12) -HL12 #HL12
+elim (tdeq_cpx_trans … HT1 … HT0) -T #T #HT1 #HT0
+/4 width=5 by fdeq_intro_dx, tdeq_trans, ex2_intro/
+qed-.