--- /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 "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.