--- /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_conversion/lpce.ma".
+include "basic_2/dynamic/cnv.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+theorem cnv_cpce_trans_lpce (h) (G):
+ ∀L1,T1,T2. ⦃G,L1⦄ ⊢ T1 ⬌η[h] T2 → ⦃G,L1⦄ ⊢ T1 !*[h] →
+ ∀L2. ⦃G,L1⦄ ⊢ ⬌η[h] L2 → ⦃G,L2⦄ ⊢ T2 !*[h].
+#h #G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
+[ #G #L1 #s #_ #L2 #_ //
+| #G #K1 #V1 #_ #Y2 #HY
+ elim (lpce_inv_pair_sn … HY) -HY #K2 #V2 #HK #HV #H destruct
\ No newline at end of file