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diff --git a/matita/matita/contribs/lambda_delta/basic_2/etc/ltpsss/lcpr_aaa.etc b/matita/matita/contribs/lambda_delta/basic_2/etc/ltpsss/lcpr_aaa.etc
new file mode 100644
index 000000000..77f384e58
--- /dev/null
+++ b/matita/matita/contribs/lambda_delta/basic_2/etc/ltpsss/lcpr_aaa.etc
@@ -0,0 +1,34 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/aaa_ltpsss.ma".
+include "basic_2/reducibility/ltpr_aaa.ma".
+include "basic_2/reducibility/cpr.ma".
+include "basic_2/reducibility/lcpr.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *************)
+
+(* Properties about atomic arity assignment on terms ************************)
+
+lemma aaa_lcpr_conf: ∀L1,T,A. L1 ⊢ T ÷ A → ∀L2. L1 ⊢ ➡ L2 → L2 ⊢ T ÷ A.
+#L1 #T #A #HT #L2 * /3 width=5/
+qed.
+
+lemma aaa_cpr_conf: ∀L,T1,A. L ⊢ T1 ÷ A → ∀T2. L ⊢ T1 ➡ T2 → L ⊢ T2 ÷ A.
+#L #T1 #A #HT1 #T2 * /3 width=5/
+qed.
+
+lemma aaa_lcpr_cpr_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2. L1 ⊢ ➡ L2 →
+                         ∀T2. L2 ⊢ T1 ➡ T2 → L2 ⊢ T2 ÷ A.
+/3 width=3/ qed.