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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_prototerm_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_prototerm_eq.ma
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index 000000000..46e539e4e
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind_k/unwind2_prototerm_eq.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(**) (* reverse include *)
+include "ground/lib/subset_ext_equivalence.ma".
+include "delayed_updating/unwind_k/unwind2_path_eq.ma".
+include "delayed_updating/unwind_k/unwind2_prototerm.ma".
+
+(* TAILED UNWIND FOR PROTOTERM **********************************************)
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma unwind2_term_eq_repl_sn (f1) (f2) (t):
+      f1 ≗ f2 → ▼[f1]t ⇔ ▼[f2]t.
+/3 width=1 by subset_equivalence_ext_f1_exteq, unwind2_path_eq_repl/
+qed.
+
+lemma unwind2_term_eq_repl_dx (f) (t1) (t2):
+      t1 ⇔ t2 → ▼[f]t1 ⇔ ▼[f]t2.
+/2 width=1 by subset_equivalence_ext_f1_bi/
+qed.