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diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqus_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqus_fqup.ma
deleted file mode 100644
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--- a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqus_fqup.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 "basic_2/s_computation/fqup.ma".
-include "basic_2/s_computation/fqus.ma".
-
-(* STAR-ITERATED SUPCLOSURE *************************************************)
-
-(* Alternative definition with plus-iterated supclosure *********************)
-
-lemma fqup_fqus: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄.
-#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
-/3 width=5 by fqus_strap1, fquq_fqus, fqu_fquq/
-qed.
-
-(* Basic_2A1: was: fqus_inv_gen *)
-lemma fqus_inv_fqup: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
-                     ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ ∨ (∧∧ G1 = G2 & L1 = L2 & T1 = T2).
-#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2 //
-#G #G2 #L #L2 #T #T2 #_ *
-[ #H2 * /3 width=5 by fqup_strap1, or_introl/
-  * /3 width=1 by fqu_fqup, or_introl/
-| * #HG #HL #HT destruct //
-]
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma fqus_strap1_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐[b] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
-#b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H1) -H1
-[ /2 width=5 by fqup_strap1/
-| * /2 width=1 by fqu_fqup/
-]
-qed-.
-
-lemma fqus_strap2_fqu: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
-#b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fqus_inv_fqup … H2) -H2
-[ /2 width=5 by fqup_strap2/
-| * /2 width=1 by fqu_fqup/
-]
-qed-.
-
-lemma fqus_fqup_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
-                       ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
-#b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 @(fqup_ind … H2) -H2 -G2 -L2 -T2
-/2 width=5 by fqus_strap1_fqu, fqup_strap1/
-qed-.
-
-lemma fqup_fqus_trans: ∀b,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G, L, T⦄ →
-                       ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
-#b #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 @(fqup_ind_dx … H1) -H1 -G1 -L1 -T1
-/3 width=5 by fqus_strap2_fqu, fqup_strap2/
-qed-.
-
-(* Advanced inversion lemmas for plus-iterated supclosure *******************)
-
-lemma fqup_inv_step_sn: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
-                        ∃∃G,L,T. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ & ⦃G, L, T⦄ ⊐*[b] ⦃G2, L2, T2⦄.
-#b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1 /2 width=5 by ex2_3_intro/
-#G1 #G #L1 #L #T1 #T #H1 #_ * /4 width=9 by fqus_strap2, fqu_fquq, ex2_3_intro/
-qed-.