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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper_inner.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper_inner.ma
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/prototerm_proper_inner.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/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 ⧸≬ 𝐈 → t ϵ 𝐏.
+/4 width=3 by path_des_outer_proper, subset_ol_i/
+qed.