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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnu_cnr_simple.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnu_cnr_simple.ma
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+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnu_cnr_simple.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/cnr.ma".
+include "basic_2/rt_transition/cnu.ma".
+
+(* NORMAL TERMS FOR T-UNUNBOUND RT-TRANSITION *******************************)
+
+(* Advanced properties with simple terms and normal terms for r-transition **)
+
+lemma cnu_appl_simple (h) (G) (L):
+      ∀V,T. ⦃G,L⦄ ⊢ ➡[h] 𝐍⦃V⦄ → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T⦄ → 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃ⓐV.T⦄.
+#h #G #L #V1 #T1 #HV1 #HT1 #HS #n #X #H
+elim (cpm_inv_appl1_simple … H HS) -H -HS #V2 #T2 #HV12 #HT12 #H destruct
+lapply (HV1 … HV12) -HV1 -HV12 #H destruct
+/3 width=2 by tueq_appl/
+qed.