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diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fle_lsubf.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fle_lsubf.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 "basic_2/static/frees_fqup.ma".
+include "basic_2/static/lsubf_lsubr.ma".
+include "basic_2/static/fle.ma".
+
+(* FREE VARIABLES INCLUSION FOR RESTRICTED CLOSURES *************************)
+
+(* Advanced forward lemmas ***************************************************)
+
+lemma fle_fwd_pair_sn: ∀I1,I2,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I1}V1, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄ →
+                       ⦃L1.ⓧ, T1⦄ ⊆ ⦃L2.ⓑ{I2}V2, T2⦄.
+#I1 #I2 #L1 #L2 #V1 #V2 #T1 #T2 *
+#n1 #n2 #f1 #f2 #Hf1 #Hf2 #HL12 #Hf12
+elim (lveq_inv_pair_pair … HL12) -HL12 #HL12 #H1 #H2 destruct
+elim (frees_total (L1.ⓧ) T1) #g1 #Hg1
+lapply (lsubr_lsubf … Hg1 … Hf1) -Hf1 /2 width=1 by lsubr_unit/ #Hfg1
+/5 width=10 by lsubf_fwd_sle, lveq_bind, sle_trans, ex4_4_intro/ (**) (* full auto too slow *)
+qed-.