--- /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/rt_transition/cpm_simple.ma".
+include "basic_2/rt_transition/cnh.ma".
+
+(* NORMAL TERMS HEAD FOR T-UNUNBOUND RT-TRANSITION **************************)
+
+(* Advanced properties with simple terms ************************************)
+
+lemma cnh_appl_simple (h) (G) (L): ∀V,T. 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃ⓐV.T⦄.
+#h #G #L #V1 #T1 #HT1 #n #X #H
+elim (cpm_inv_appl1_simple … H HT1) -H -HT1 #V2 #T2 #_ #_ #H destruct
+/1 width=1 by theq_pair/
+qed.