--- /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/path_inner.ma".
+include "delayed_updating/syntax/path_proper.ma".
+
+(* INNER CONDITION FOR PATH *************************************************)
+
+(* Destructions with proper condition for path ******************************)
+
+lemma path_des_outer_proper (p):
+ p β§ΈΟ΅ π β p Ο΅ π.
+#p #H1 #H2 destruct
+@H1 -H1 // (**) (* auto fails *)
+qed-.