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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lsuba.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_lsuba.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/dynamic/snv_aaa.ma".
+include "basic_2/dynamic/lsubsv.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
+
+(* Properties on local environment refinement for atomic arity assignment ***)
+
+lemma lsubsv_fwd_lsuba: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 → L1 ⁝⊑ L2.
+#h #g #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
+#L1 #L2 #V1 #V2 #W1 #W2 #l #HV1 #HVW1 #HW12 #HW2 #_ #_ #HL12
+elim (snv_fwd_aaa … HV1) -HV1 #A #HV1
+elim (snv_fwd_aaa … HW2) -HW2 #B #HW2
+lapply (ssta_aaa … HV1 … HVW1) -HVW1 #H1
+lapply (lsuba_aaa_trans … HW2 … HL12) #H2
+lapply (aaa_cpcs_mono … HW12 … H1 … H2) -W1 -H2 #H destruct /2 width=3/
+qed-.