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diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/s_computation/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 "ground_2/lib/star.ma".
-include "basic_2/notation/relations/suptermplus_6.ma".
-include "basic_2/notation/relations/suptermplus_7.ma".
-include "basic_2/s_transition/fqu.ma".
-
-(* PLUS-ITERATED SUPCLOSURE *************************************************)
-
-definition fqup: bool → tri_relation genv lenv term ≝
-                 λb. tri_TC … (fqu b).
-
-interpretation "extended plus-iterated structural successor (closure)"
-   'SupTermPlus b G1 L1 T1 G2 L2 T2 = (fqup b G1 L1 T1 G2 L2 T2).
-
-interpretation "plus-iterated structural successor (closure)"
-   'SupTermPlus G1 L1 T1 G2 L2 T2 = (fqup true G1 L1 T1 G2 L2 T2).
-
-(* Basic properties *********************************************************)
-
-lemma fqu_fqup: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
-                ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄.
-/2 width=1 by tri_inj/ qed.
-
-lemma fqup_strap1: ∀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⦄.
-/2 width=5 by tri_step/ qed.
-
-lemma fqup_strap2: ∀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⦄.
-/2 width=5 by tri_TC_strap/ qed.
-
-lemma fqup_pair_sn: ∀b,I,G,L,V,T. ⦃G, L, ②{I}V.T⦄ ⊐+[b] ⦃G, L, V⦄.
-/2 width=1 by fqu_pair_sn, fqu_fqup/ qed.
-
-lemma fqup_bind_dx: ∀b,p,I,G,L,V,T. ⦃G, L, ⓑ{p,I}V.T⦄ ⊐+[b] ⦃G, L.ⓑ{I}V, T⦄.
-/2 width=1 by fqu_bind_dx, fqu_fqup/ qed.
-
-lemma fqup_clear: ∀p,I,G,L,V,T. ⦃G, L, ⓑ{p,I}V.T⦄ ⊐+[Ⓕ] ⦃G, L.ⓧ, T⦄.
-/3 width=1 by fqu_clear, fqu_fqup/ qed.
-
-lemma fqup_flat_dx: ∀b,I,G,L,V,T. ⦃G, L, ⓕ{I}V.T⦄ ⊐+[b] ⦃G, L, T⦄.
-/2 width=1 by fqu_flat_dx, fqu_fqup/ qed.
-
-lemma fqup_flat_dx_pair_sn: ∀b,I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.②{I2}V2.T⦄ ⊐+[b] ⦃G, L, V2⦄.
-/2 width=5 by fqu_pair_sn, fqup_strap1/ qed.
-
-lemma fqup_bind_dx_flat_dx: ∀b,p,G,I1,I2,L,V1,V2,T. ⦃G, L, ⓑ{p,I1}V1.ⓕ{I2}V2.T⦄ ⊐+[b] ⦃G, L.ⓑ{I1}V1, T⦄.
-/2 width=5 by fqu_flat_dx, fqup_strap1/ qed.
-
-lemma fqup_flat_dx_bind_dx: ∀b,p,I1,I2,G,L,V1,V2,T. ⦃G, L, ⓕ{I1}V1.ⓑ{p,I2}V2.T⦄ ⊐+[b] ⦃G, L.ⓑ{I2}V2, T⦄.
-/2 width=5 by fqu_bind_dx, fqup_strap1/ qed.
-
-(* Basic eliminators ********************************************************)
-
-lemma fqup_ind: ∀b,G1,L1,T1. ∀Q:relation3 ….
-                (∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
-                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G L T → Q G2 L2 T2) →
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G2 L2 T2.
-#b #G1 #L1 #T1 #Q #IH1 #IH2 #G2 #L2 #T2 #H
-@(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
-qed-.
-
-lemma fqup_ind_dx: ∀b,G2,L2,T2. ∀Q:relation3 ….
-                   (∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → Q G1 L1 T1) →
-                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ⊐[b] ⦃G, L, T⦄ → ⦃G, L, T⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G L T → Q G1 L1 T1) →
-                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ → Q G1 L1 T1.
-#b #G2 #L2 #T2 #Q #IH1 #IH2 #G1 #L1 #T1 #H
-@(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
-qed-.
-
-(* Basic_2A1: removed theorems 1: fqup_drop *)