--- /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/lsuba.ma".
+include "Basic_2/computation/acp_aaa.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
+
+(* properties concerning lenv refinement for atomic arity assignment ********)
+
+lemma lsubc_lsuba: ∀RR,RS,RP. acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
+ ∀L1,L2. L1 ÷⊑ L2 → L1 [RP] ⊑ L2.
+#RR #RS #RP #H1RP #H2RP #L1 #L2 #H elim H -L1 -L2
+// /2 width=1/ /3 width=4/
+qed.