--- /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_computation/cpms_cnu.ma".
+include "basic_2/rt_computation/cpmue.ma".
+include "basic_2/dynamic/cnv_preserve.ma".
+
+(* T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS ******************)
+
+(* Properties with evaluation for t-unbound rt-transition on terms **********)
+
+lemma cnv_cpmue_trans (a) (h) (G) (L):
+ ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
+ ∀T2,n. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T2 ![a,h].
+/3 width=4 by cpmue_fwd_cpms, cnv_cpms_trans/ qed-.
+
+lemma cnv_cpmue_cpms_conf (a) (h) (G) (L):
+ ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[n1,h] T1 →
+ ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃T2⦄ →
+ ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[h,n2-n1] 𝐍*⦃T⦄ & T2 ≅ T.
+#a #h #G #L #T0 #HT0 #T1 #n1 #HT01 #T2 #n2 * #HT02 #HT2
+elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
+lapply (cpms_inv_cnu_sn … HT20 HT2) -HT20 #HT20
+/4 width=8 by cpmue_intro, cnu_tueq_trans, ex2_intro/
+qed-.
+
+(* Main properties with evaluation for t-unbound rt-transition on terms *****)
+
+theorem cnv_cpmue_mono (a) (h) (G) (L):
+ ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] → ∀T1,n1. ⦃G,L⦄ ⊢ T0 ➡*[h,n1] 𝐍*⦃T1⦄ →
+ ∀T2,n2. ⦃G,L⦄ ⊢ T0 ➡*[h,n2] 𝐍*⦃T2⦄ → T1 ≅ T2.
+#a #h #G #L #T0 #HT0 #T1 #n1 * #HT01 #HT1 #T2 #n2 * #HT02 #HT2
+elim (cnv_cpms_conf … HT0 … HT01 … HT02) -T0 #T0 #HT10 #HT20
+/3 width=8 by cpms_inv_cnu_sn, tueq_canc_dx/
+qed-.