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diff --git a/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csups_csups.etc b/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csups_csups.etc
new file mode 100644
index 000000000..aa54d9bef
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+++ b/matita/matita/contribs/lambda_delta/basic_2/etc/csup/csups_csups.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 "basic_2/substitution/csup_csup.ma".
+include "basic_2/unfold/csups.ma".
+
+(* STAR-ITERATED SUPCLOSURE *************************************************)
+
+(* Advanced forward lemmas **************************************************)
+
+(*
+lemma csupp_strap2_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ > ⦃L0, T2⦄ →
+                             ∀T3. ⦃L0, T2⦄ >+ ⦃L, T3⦄ →
+                             L = L0 ∨ ⦃L, T1⦄ >+ ⦃L, T3⦄.
+#L #L0 #T1 #T2 * -L -L0 -T1 -T2 /2 width=1/
+[ #I #L0 #K0 #V0 #i #HLK0 #T3 #H
+  lapply (ldrop_pair2_fwd_cw … HLK0 T3) -HLK0 #H1
+  lapply (csupp_fwd_cw … H) -H #H2
+  lapply (transitive_lt … H1 H2) -H1 -H2 #H
+  elim (lt_refl_false … H)
+| #a #I #L0 #V2 #T2 #T3 #HT23
+  /3 width=5/
+
+  elim (csup_inv_ldrop … HT23 I V2 0 ?) -HT23 // #H1 #H2 destruct /2 width=1/
+  qed-.
+
+
+
+
+
+
+
+
+lemma csups_strap1_fwd_refl: ∀L,L0,T1,T2. ⦃L, T1⦄ >* ⦃L0, T2⦄ →
+                             ∀T3. ⦃L0, T2⦄ > ⦃L, T3⦄ → L = L0.
+#L #L0 #T1 #T2 #H @(csups_ind_dx … H) -L -T1 //
+#L1 #L #T1 #T #HL1 #_ #IHL0 #T3 #HL0
+lapply (csup_trans_fwd_refl … HL10) … HL0) -T2
+*) 
+lemma lift_csups_trans_aux: ∀T1,U1,d,e. ⇧[d, e] T1 ≡ U1 →
+                            ∀L1,L2,U2. ⦃L1, U1⦄ >* ⦃L2, U2⦄ → L1 = L2 →
+                            ∃T2. ⇧[d, e] T2 ≡ U2.
+#T1 #U1 #d #e #HTU1 #L1 #L2 #U2 #H @(csups_ind … H) -L2 -U2 /2 width=2/ -T1
+#L #L2 #U #U2 #HL1 #HL2 #IHL1 #H destruct
+
+* -T1 -U1 -d -e
+
+(* Main propertis ***********************************************************)
+
+theorem csups_trans: bi_transitive … csups.
+/2 width=4/ qed.