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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_simple.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cnuw_simple.ma
new file mode 100644
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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 "static_2/syntax/tweq_simple.ma".
+include "basic_2/rt_computation/cpms_cpms.ma".
+include "basic_2/rt_computation/cnuw.ma".
+
+(* NORMAL TERMS FOR T-UNUNBOUND WHD RT-TRANSITION ***************************)
+
+(* Advanced forward lemma with with simple terms ****************************)
+(*
+lemma cnuw_fwd_appl_simple (h) (G) (L):
+      ∀V,T. ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓐV.T → 𝐒⦃T⦄.
+#h #G #L #V #T #HT
+elim (simple_dec_ex T) [ // ] * #p #I #W #U #H destruct
+*)
+(* Advanced properties with simple terms ************************************)
+
+lemma cnuw_appl_simple (h) (G) (L):
+      ∀V,T. 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] ⓐV.T.
+#h #G #L #V1 #T1 #H1T1 #H2T1 #n #X #H
+elim (cpms_inv_appl_sn … H) -H *
+[ #V2 #T2 #_ #HT12 #H destruct -H1T1
+  /3 width=2 by tweq_appl/
+| #n1 #n2 #p #V2 #T2 #HT12 #_ #_ -n -n2
+  lapply (H2T1 … HT12) -H2T1 -n1 #H
+  lapply (tweq_simple_trans … H H1T1) -H -H1T1 #H
+  elim (simple_inv_bind … H)
+| #n1 #n2 #p #V2 #W2 #W #T2 #_ #_ #HT12 #_ #_ -n -n2 -V2 -W2
+  lapply (H2T1 … HT12) -H2T1 -n1 #H
+  lapply (tweq_simple_trans … H H1T1) -H -H1T1 #H
+  elim (simple_inv_bind … H)
+]
+qed.