--- /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/cpce.ma".
+include "basic_2/dynamic/cnv_preserve.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+theorem cnv_cpce_mono (a) (h) (G) (L) (T):
+ ∀T1. ⦃G,L⦄ ⊢ T ⬌η[h] T1 → ⦃G,L⦄ ⊢ T ![a,h] →
+ ∀T2. ⦃G,L⦄ ⊢ T ⬌η[h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2.
+#h #G #L #T @(fqup_wf_ind (Ⓣ) … G L T) -G -L -T
+#G0 #L0 #T0 #IH #T1
+@(insert_eq_0 … G0) #G
+@(insert_eq_0 … L0) #L
+@(insert_eq_0 … T0) #T
+* -G -L -T
+[ #G #L1 #s #_ #_ #_ #_ #L2 #_ //