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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/snta/lsubsn_cpcs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/snta/lsubsn_cpcs.etc
new file mode 100644
index 000000000..38f7e17bd
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/snta/lsubsn_cpcs.etc
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/equivalence/cpcs_cpcs.ma".
+include "basic_2/dynamic/lsubsn.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE TYPE ASSIGNMENT *******)
+
+(* Properties on context-sensitive parallel equivalence for terms ***********)
+
+lemma cpr_lsubsn_trans: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
+                        ∀T1,T2. L2 ⊢ T1 ➡ T2 → L1 ⊢ T1 ➡ T2.
+/3 width=5 by lsubsn_fwd_lsubs2, cpr_lsubs_trans/ qed-.
+
+lemma cprs_lsubsn_trans: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
+                         ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
+/3 width=5 by lsubsn_fwd_lsubs2, cprs_lsubs_trans/ qed-.
+
+lemma cpcs_lsubsn_trans: ∀h,L1,L2. h ⊢ L1 :⊑[] L2 →
+                         ∀T1,T2. L2 ⊢ T1 ⬌* T2 → L1 ⊢ T1 ⬌* T2.
+/3 width=5 by lsubsn_fwd_lsubs2, cpcs_lsubs_trans/ qed-.