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diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle.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/relocation/rtmap_id.ma".
+include "static_2/notation/relations/subseteq_4.ma".
+include "static_2/syntax/lveq.ma".
+include "static_2/static/frees.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+definition fsle: bi_relation lenv term ≝ λL1,T1,L2,T2.
+                 ∃∃n1,n2,f1,f2. L1 ⊢ 𝐅*⦃T1⦄ ≘ f1 & L2 ⊢ 𝐅*⦃T2⦄ ≘ f2 &
+                                L1 ≋ⓧ*[n1, n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
+
+interpretation "free variables inclusion (restricted closure)"
+   'SubSetEq L1 T1 L2 T2 = (fsle L1 T1 L2 T2).
+
+interpretation "free variables inclusion (term)"
+   'subseteq T1 T2 = (fsle LAtom T1 LAtom T2).
+
+(* Basic properties *********************************************************)
+
+lemma fsle_sort: ∀L,s1,s2. ⦃L, ⋆s1⦄ ⊆ ⦃L, ⋆s2⦄.
+/3 width=8 by frees_sort, sle_refl, ex4_4_intro/ qed.
+
+lemma fsle_gref: ∀L,l1,l2. ⦃L, §l1⦄ ⊆ ⦃L, §l2⦄.
+/3 width=8 by frees_gref, sle_refl, ex4_4_intro/ qed.