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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner_proper.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 ⧸ϵ 𝐈 → p ϵ 𝐏.
+#p #H1 #H2 destruct
+@H1 -H1 // (**) (* auto fails *)
+qed-.