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diff --git a/matita/matita/contribs/lambdadelta/basic_2A/static/lsubd_lsubd.ma b/matita/matita/contribs/lambdadelta/basic_2A/static/lsubd_lsubd.ma
new file mode 100644
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@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2A/static/lsubd_da.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR DEGREE ASSIGNMENT ***********************)
+
+(* Main properties **********************************************************)
+
+theorem lsubd_trans: ∀h,g,G. Transitive … (lsubd h g G).
+#h #g #G #L1 #L #H elim H -L1 -L
+[ #X #H >(lsubd_inv_atom1 … H) -H //
+| #I #L1 #L #Y #HL1 #IHL1 #X #H
+  elim (lsubd_inv_pair1 … H) -H * #L2
+  [ #HL2 #H destruct /3 width=1 by lsubd_pair/
+  | #W #V #d #HV #HW #HL2 #H1 #H2 #H3 destruct
+    /3 width=3 by lsubd_beta, lsubd_da_trans/
+  ]
+| #L1 #L #W #V #d #HV #HW #HL1 #IHL1 #X #H
+  elim (lsubd_inv_pair1 … H) -H * #L2
+  [ #HL2 #H destruct /3 width=5 by lsubd_beta, lsubd_da_conf/
+  | #W0 #V0 #d0 #_ #_ #_ #H destruct
+  ]
+]
+qed-.