--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||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_drops.ma".
+include "basic_2/s_computation/fqus_fqup.ma".
+
+(* STAR-ITERATED SUPCLOSURE *************************************************)
+
+(* Properties with generic slicing for local environments *******************)
+
+lemma fqus_drops: ∀G,L,K,T,U,l. ⬇*[l] L ≡ K → ⬆*[l] T ≡ U →
+ ⦃G, L, U⦄ ⊐* ⦃G, K, T⦄.
+#G #L #K #T #U * /3 width=3 by fqup_drops_succ, fqup_fqus/
+#HLK #HTU <(lifts_fwd_isid … HTU) -U // <(drops_fwd_isid … HLK) -K //
+qed.