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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnh_lifts.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnh_lifts.ma
new file mode 100644
index 000000000..3bbfeee85
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnh_lifts.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 "static_2/relocation/lifts.ma".
+include "basic_2/rt_transition/cnh.ma".
+
+(* NORMAL TERMS FOR HEAD T-UNUNBOUND RT-TRANSITION **************************)
+
+(* Advanced properties with uniform relocation for terms ********************)
+
+lemma cnh_lref (h) (I) (G) (L):
+      ∀i. ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃#i⦄ → ⦃G,L.ⓘ{I}⦄ ⊢ ⥲[h] 𝐍⦃#↑i⦄.
+#h #I #G #L #i #Hi #n #X #H
+elim (cpm_inv_lref1 … H) -H *
+[ #H #_ destruct //
+| #J #K #V #HV #HVX #H destruct
+  lapply (Hi … HV) -Hi -HV #HV
+  lapply (theq_inv_lref1 … HV) -HV #H destruct
+  lapply (lifts_inv_lref1_uni … HVX) -HVX #H destruct //
+]
+qed.