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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fsup/fsups.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fsup/fsups.etc
index c7867e1f8..36abe1208 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/fsup/fsups.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/fsup/fsups.etc
@@ -1,92 +1,29 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/grammar/fsupp.ma".
-
-(* STAR-ITERATED SUPCLOSURE *************************************************)
-
-definition fsups: bi_relation lenv term ≝ bi_star … fsup.
-
-interpretation "star-iterated structural successor (closure)"
-   'SupTermStar L1 T1 L2 T2 = (fsups L1 T1 L2 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma fsups_ind: ∀L1,T1. ∀R:relation2 lenv term. R L1 T1 →
-                 (∀L,L2,T,T2. ⦃L1, T1⦄ ⊃* ⦃L, T⦄ → ⦃L, T⦄ ⊃ ⦃L2, T2⦄ → R L T → R L2 T2) →
-                 ∀L2,T2. ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄ → R L2 T2.
-#L1 #T1 #R #IH1 #IH2 #L2 #T2 #H
-@(bi_star_ind … IH1 IH2 ? ? H)
-qed-.
-
-lemma fsups_ind_dx: ∀L2,T2. ∀R:relation2 lenv term. R L2 T2 →
-                    (∀L1,L,T1,T. ⦃L1, T1⦄ ⊃ ⦃L, T⦄ → ⦃L, T⦄ ⊃* ⦃L2, T2⦄ → R L T → R L1 T1) →
-                    ∀L1,T1. ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄ → R L1 T1.
-#L2 #T2 #R #IH1 #IH2 #L1 #T1 #H
-@(bi_star_ind_dx … IH1 IH2 ? ? H)
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma fsups_refl: bi_reflexive … fsups.
-/2 width=1/ qed.
-
-lemma fsupp_fsups: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄.
-/2 width=1/ qed.
-
-lemma fsup_fsups: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄.
-/2 width=1/ qed.
-
-lemma fsups_strap1: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃* ⦃L, T⦄ → ⦃L, T⦄ ⊃ ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma fsups_strap2: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃ ⦃L, T⦄ → ⦃L, T⦄ ⊃* ⦃L2, T2⦄ →
-                    ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma fsups_fsupp_fsupp: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃* ⦃L, T⦄ →
-                         ⦃L, T⦄ ⊃+ ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-lemma fsupp_fsups_fsupp: ∀L1,L,L2,T1,T,T2. ⦃L1, T1⦄ ⊃+ ⦃L, T⦄ →
-                         ⦃L, T⦄ ⊃* ⦃L2, T2⦄ → ⦃L1, T1⦄ ⊃+ ⦃L2, T2⦄.
-/2 width=4/ qed.
-
-(* Basic forward lemmas *****************************************************)
-
-lemma fsups_fwd_cw: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄ → ♯{L2, T2} ≤ ♯{L1, T1}.
-#L1 #L2 #T1 #T2 #H @(fsups_ind … H) -L2 -T2 //
-/4 width=3 by fsup_fwd_cw, lt_to_le_to_lt, lt_to_le/ (**) (* slow even with trace *)
-qed-.
-
 (* Advanced inversion lemmas on plus-iterated supclosure ********************)
 
-lemma fsupp_inv_bind1_fsups: ∀b,J,L1,L2,W,U,T2. ⦃L1, ⓑ{b,J}W.U⦄ ⊃+ ⦃L2, T2⦄ →
-                             ⦃L1, W⦄ ⊃* ⦃L2, T2⦄ ∨ ⦃L1.ⓑ{J}W, U⦄ ⊃* ⦃L2, T2⦄.
-#b #J #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -L2 -T2
-[ #L2 #T2 #H
-  elim (fsup_inv_bind1 … H) -H * #H1 #H2 destruct /2 width=1/
-| #L #T #L2 #T2 #_ #HT2 * /3 width=4/
+lamma fsupp_inv_bind1_fsups: ∀b,J,G1,G2,L1,L2,W,U,T2. ⦃G1, L1, ⓑ{b,J}W.U⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                             ⦃G1, L1, W⦄ ⊃* ⦃G2, L2, T2⦄ ∨ ⦃L1.ⓑ{J}W, U⦄ ⊃* ⦃G2, L2, T2⦄.
+#b #J #G1 #G2 #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -G2 -L2 -T2
+[ #G2 #L2 #T2 #H
+  elim (fsup_inv_bind1 … H) -H * #H1 #H2 #H3 destruct /2 width=1/
+| #G #G2 #L #L2 #T #T2 #_ #HT2 * /3 width=4/
 ]
-qed-.
+qad-.
 
-lemma fsupp_inv_flat1_fsups: ∀J,L1,L2,W,U,T2. ⦃L1, ⓕ{J}W.U⦄ ⊃+ ⦃L2, T2⦄ →
-                             ⦃L1, W⦄ ⊃* ⦃L2, T2⦄ ∨ ⦃L1, U⦄ ⊃* ⦃L2, T2⦄.
-#J #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -L2 -T2
-[ #L2 #T2 #H
+lamma fsupp_inv_flat1_fsups: ∀J,G1,G2,L1,L2,W,U,T2. ⦃G1, L1, ⓕ{J}W.U⦄ ⊃+ ⦃G2, L2, T2⦄ →
+                             ⦃G1, L1, W⦄ ⊃* ⦃G2, L2, T2⦄ ∨ ⦃G1, L1, U⦄ ⊃* ⦃G2, L2, T2⦄.
+#J #G1 #G2 #L1 #L2 #W #U #T2 #H @(fsupp_ind … H) -G2 -L2 -T2
+[ #G2 #L2 #T2 #H
   elim (fsup_inv_flat1 … H) -H #H1 * #H2 destruct /2 width=1/
-| #L #T #L2 #T2 #_ #HT2 * /3 width=4/
+| #G #G2 #L #L2 #T #T2 #_ #HT2 * /3 width=4/
 ]
-qed-.
+qad-.
+
+lamma fsupp_fsups: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊃* ⦃G2, L2, T2⦄.
+/2 width=1 by tri_inj/ qed.
+
+lamma fsups_lref: ∀I,G,K,V,i,L. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊃* ⦃G, K, V⦄.
+/3 width=5 by _/ qed.
+
+lamma fsups_lref_S_lt: ∀I,G1,G2,L,K,V,T,i.
+                       0 < i → ⦃G1, L, #(i-1)⦄ ⊃* ⦃G2, K, T⦄ → ⦃G1, L.ⓑ{I}V, #i⦄ ⊃+ ⦃G2, K, T⦄.
+/3 width=7 by _/ qed.