--- /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 "delayed_updating/syntax/prototerm_proper.ma".
+include "delayed_updating/syntax/path_inner_proper.ma".
+include "ground/lib/subset_overlap.ma".
+
+(* PROPER CONDITION FOR PROTOTERM *******************************************)
+
+(* Constructions with inner condition for prototerm *************************)
+
+lemma term_proper_outer (t):
+ t β§Έβ¬ π β t Ο΅ π.
+/4 width=3 by path_des_outer_proper, subset_ol_i/
+qed.