--- /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/notation/relations/predevalstar_6.ma".
+include "basic_2/rt_transition/cnu.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS ******************)
+
+definition cpmue (h) (n) (G) (L): relation2 term term ≝
+ λT1,T2. ∧∧ ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T2⦄.
+
+interpretation "t-unbound evaluation for t-bound context-sensitive parallel rt-transition (term)"
+ 'PRedEvalStar h n G L T1 T2 = (cpmue h n G L T1 T2).
+
+definition R_cpmue (h) (G) (L) (T): predicate nat ≝
+ λn. ∃U. ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃U⦄.
+
+(* Basic properties *********************************************************)
+
+lemma cpmue_intro (h) (n) (G) (L):
+ ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄.
+/2 width=1 by conj/ qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpmue_fwd_cpms (h) (n) (G) (L):
+ ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2.
+#h #n #G #L #T1 #T2 * #HT12 #_ //
+qed-.