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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc
new file mode 100644
index 000000000..838c7b6d4
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/sstas/sstas_lift.etc
@@ -0,0 +1,57 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/ssta_lift.ma".
+include "basic_2/unwind/sstas.ma".
+
+(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENTON TERMS ***********************)
+
+(* Advanced properties ******************************************************)
+
+lemma sstas_total_S: ∀h,g,L,l,T,U. ⦃h, L⦄ ⊢ T•[g, l + 1]U →
+                     ∃∃W. ⦃h, L⦄ ⊢ T •*[g] W & ⦃h, L⦄ ⊢ U •*[g] W.
+#h #g #L #l @(nat_ind_plus … l) -l
+[ #T #U #HTU
+  elim (ssta_fwd_correct … HTU) /4 width=4/
+| #l #IHl #T #U #HTU
+  elim (ssta_fwd_correct … HTU) <minus_plus_m_m #V #HUV
+  elim (IHl … HUV) -IHl -HUV /3 width=4/
+]
+qed-.
+
+(* Properties on relocation *************************************************)
+
+lemma sstas_lift: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
+                  ∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
+                  ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 •*[g] U2.
+#h #g #L1 #T1 #U1 #H @(sstas_ind_alt … H) -T1
+[ #T1 #HUT1 #L2 #d #e #HL21 #X #HX #U2 #HU12
+  >(lift_mono … HX … HU12) -X
+  elim (lift_total T1 d e) /3 width=10/
+| #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL21 #T2 #HT02 #U2 #HU12
+  elim (lift_total U0 d e) /3 width=10/
+]
+qed.
+
+lemma sstas_inv_lift1: ∀h,g,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 →
+                       ∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
+                       ∃∃U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 & ⇧[d, e] U1 ≡ U2.
+#h #g #L2 #T2 #U2 #H @(sstas_ind_alt … H) -T2
+[ #T2 #HUT2 #L1 #d #e #HL21 #U1 #HU12
+  elim (ssta_inv_lift1 … HUT2 … HL21 … HU12) -HUT2 -HL21 /3 width=3/
+| #T0 #U0 #l0 #HTU0 #_ #IHU01 #L1 #d #e #HL21 #U1 #HU12
+  elim (ssta_inv_lift1 … HTU0 … HL21 … HU12) -HTU0 -HU12 #U #HU1 #HU0
+  elim (IHU01 … HL21 … HU0) -IHU01 -HL21 -U0 /3 width=4/
+]
+qed-.