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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected_zero.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected_zero.ma
deleted file mode 100644
index 5b3631f9c..000000000
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr_unprotected_zero.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/reduction/dbfr_constructors.ma".
-include "delayed_updating/reduction/ibfr_constructors.ma".
-include "delayed_updating/unwind/unwind2_prototerm_constructors.ma".
-include "delayed_updating/substitution/lift_prototerm_constructors.ma".
-include "ground/arith/pnat_two.ma".
-
-(* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
-
-(* Example of unprotected balanced β-reduction ******************************)
-
-definition l3_t: prototerm ≝
-           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).⧣𝟏).
-
-definition l3_i1: prototerm ≝
-           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛌.⧣𝟏).
-
-definition l3_i2: prototerm ≝
-           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛌.⧣↑𝟐).
-
-definition l3_i2': prototerm ≝
-           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛌.⧣↑↑𝟐).
-
-definition l3_d1: prototerm ≝
-           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛕𝟏.(𝛌.⧣𝟏)).
-
-definition l3_d2: prototerm ≝
-           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛕𝟏.𝛌.(⧣𝟐)).
-
-definition l3_d2': prototerm ≝
-           (𝛌.＠(𝛌.⧣𝟏).𝛌.＠(⧣𝟐).𝛕𝟏.𝛌.𝛕𝟏.(⧣𝟐)).
-
-lemma l3_ti1:
-      l3_t ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝐞] l3_i1.
-@ibfr_abst_hd
-@ibfr_eq_trans
-[ | @(ibfr_beta_0 … (𝟎))
-  [ /2 width=1 by pcc_A_sn, pcc_empty/
-  | >list_append_lcons_sn /2 width=1 by in_comp_appl_hd/
-  ]
-]
-@appl_eq_repl [ // ]
-@abst_eq_repl
-@(subset_eq_canc_sn … (fsubst_appl_hd …))
-@appl_eq_repl [ // ]
-@(subset_eq_canc_sn … (fsubst_empty_rc …))
-@(subset_eq_canc_sn … (lift_term_abst …))
-@abst_eq_repl
-@(subset_eq_canc_sn … (lift_term_oref_pap … )) //
-qed.
-
-lemma l3_i12:
-      l3_i1 ➡𝐢𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝗟◗𝐞] l3_i2.
-@ibfr_abst_hd
-@ibfr_appl_hd
-@ibfr_abst_hd
-@ibfr_eq_trans [| @ibfr_beta_0 // ]
-@appl_eq_repl [ // ]
-@abst_eq_repl
-@(subset_eq_canc_sn … (fsubst_empty_rc …))
-@(subset_eq_canc_sn … (lift_term_oref_pap … )) //
-qed.
-
-lemma l3_td1:
-      l3_t ➡𝐝𝐛𝐟[𝗟◗𝗔◗𝗟◗𝗔◗𝐞] l3_d1.
-@dbfr_abst_hd
-@dbfr_eq_trans
-[ | @(dbfr_beta_0 … (𝟎))
-  [ /2 width=1 by pcc_A_sn, pcc_empty/
-  | >list_append_lcons_sn /2 width=1 by in_comp_appl_hd/
-  ]
-]
-@appl_eq_repl [ // ]
-@abst_eq_repl
-@(subset_eq_canc_sn … (fsubst_appl_hd …))
-@appl_eq_repl [ // ]
-@(subset_eq_canc_sn … (fsubst_empty_rc …))
-@iref_eq_repl //
-qed.
-
-lemma l3_di2:
-      l3_i2 ⇔ ▼[𝐢]l3_d2.
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
-[ @(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-  @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-]
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
-[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-]
-@(subset_eq_canc_sn … (unwind2_term_iref …))
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-qed.
-
-lemma l3_di2':
-      l3_i2' ⇔ ▼[𝐢]l3_d2'.
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
-[ @(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-  @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-]
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(subset_eq_canc_sn … (unwind2_term_appl …)) @appl_eq_repl
-[ @(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-]
-@(subset_eq_canc_sn … (unwind2_term_iref …))
-@(subset_eq_canc_sn … (unwind2_term_abst …)) @abst_eq_repl
-@(subset_eq_canc_sn … (unwind2_term_iref …))
-@(subset_eq_canc_sn … (unwind2_term_oref_pap …)) //
-qed.