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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_prototerm_eq.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_prototerm_eq.etc
deleted file mode 100644
index 0b3ba39b0..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_prototerm_eq.etc
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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 "ground/lib/subset_ext_equivalence.ma".
-include "delayed_updating/substitution/lift_path_after.ma".
-include "delayed_updating/substitution/lift_prototerm.ma".
-
-(* LIFT FOR PROTOTERM *******************************************************)
-
-(* Constructions with subset_equivalence ************************************)
-
-lemma lift_term_eq_repl_sn (f1) (f2) (t):
-      f1 ≗ f2 → ↑[f1]t ⇔ ↑[f2]t.
-/3 width=1 by subset_equivalence_ext_f1_exteq, lift_path_eq_repl/
-qed.
-
-lemma lift_term_eq_repl_dx (f) (t1) (t2):
-      t1 ⇔ t2 → ↑[f]t1 ⇔ ↑[f]t2.
-/2 width=1 by subset_equivalence_ext_f1_bi/
-qed.
-
-lemma lift_term_after (f1) (f2) (t):
-      ↑[f2]↑[f1]t ⇔ ↑[f2∘f1]t.
-#f1 #f2 #t @subset_eq_trans
-[
-| @subset_inclusion_ext_f1_compose
-| @subset_equivalence_ext_f1_exteq /2 width=5/
-]
-qed.
-
-lemma lift_term_id_sn (t):
-      t ⊆ ↑[𝐢]t.
-#t #p #Hp
->(lift_path_id p)
-/2 width=1 by in_comp_lift_bi/
-qed-.
-
-lemma lift_term_id_dx (t):
-      ↑[𝐢]t ⊆ t.
-#t #p * #q #Hq #H destruct //
-qed-.
-
-lemma lift_term_id (t):
-      t ⇔ ↑[𝐢]t.
-/3 width=2 by lift_term_id_dx, lift_term_id_sn, conj/
-qed.