--- /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/static/lsubd.ma".
+include "basic_2/dynamic/lsubsv.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
+
+(* Forward lemmas on lenv refinement for degree assignment ******************)
+
+lemma lsubsv_fwd_lsubd: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 → G ⊢ L1 ▪⊑[h, g] L2.
+#h #g #G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/ /2 width=3/
+qed-.