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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpmuwe.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpmuwe.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/notation/relations/predevalwstar_6.ma".
+include "basic_2/rt_computation/cnuw.ma".
+
+(* T-UNBOUND WHD EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS **************)
+
+definition cpmuwe (h) (n) (G) (L): relation2 term term ≝
+           λT1,T2. ∧∧ ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T2.
+
+interpretation "t-unbound whd evaluation for t-bound context-sensitive parallel rt-transition (term)"
+   'PRedEvalWStar h n G L T1 T2 = (cpmuwe h n G L T1 T2).
+
+definition R_cpmuwe (h) (G) (L) (T): predicate nat ≝
+           λn. ∃U. ⦃G,L⦄ ⊢ T ➡*𝐍𝐖*[h,n] U.
+
+(* Basic properties *********************************************************)
+
+lemma cpmuwe_intro (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ ➡𝐍𝐖*[h] T2 → ⦃G,L⦄ ⊢ T1 ➡*𝐍𝐖*[h,n] T2.
+/2 width=1 by conj/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma cpmuwe_sort (h) (n) (G) (L) (T):
+      ∀s. ⦃G,L⦄ ⊢ T ➡*[n,h] ⋆s → ⦃G,L⦄ ⊢ T ➡*𝐍𝐖*[h,n] ⋆s.
+/3 width=5 by cnuw_sort, cpmuwe_intro/ qed.
+
+lemma cpmuwe_ctop (h) (n) (G) (T):
+      ∀i. ⦃G,⋆⦄ ⊢ T ➡*[n,h] #i → ⦃G,⋆⦄ ⊢ T ➡*𝐍𝐖*[h,n] #i.
+/3 width=5 by cnuw_ctop, cpmuwe_intro/ qed.
+
+lemma cpmuwe_zero_unit (h) (n) (G) (L) (T):
+      ∀I. ⦃G,L.ⓤ{I}⦄ ⊢ T ➡*[n,h] #0 → ⦃G,L.ⓤ{I}⦄ ⊢ T ➡*𝐍𝐖*[h,n] #0.
+/3 width=6 by cnuw_zero_unit, cpmuwe_intro/ qed.
+
+lemma cpmuwe_gref (h) (n) (G) (L) (T):
+      ∀l. ⦃G,L⦄ ⊢ T ➡*[n,h] §l → ⦃G,L⦄ ⊢ T ➡*𝐍𝐖*[h,n] §l.
+/3 width=5 by cnuw_gref, cpmuwe_intro/ qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpmuwe_fwd_cpms (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2.
+#h #n #G #L #T1 #T2 * #HT12 #_ //
+qed-.