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diff --git a/matita/matita/contribs/lambda_delta/basic_2/computation/lsubc_ldrops.ma b/matita/matita/contribs/lambda_delta/basic_2/computation/lsubc_ldrops.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/computation/lsubc_ldrop.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR ABSTRACT CANDIDATES OF REDUCIBILITY *****)
+
+(* Properties concerning generic local environment slicing ******************)
+
+(* Basic_1: was: csubc_drop1_conf_rev *)
+lemma ldrops_lsubc_trans: ∀RR,RS,RP.
+                          acp RR RS RP → acr RR RS RP (λL,T. RP L T) →
+                          ∀L1,K1,des. ⇩*[des] L1 ≡ K1 → ∀K2. K1 [RP] ⊑ K2 →
+                          ∃∃L2. L1 [RP] ⊑ L2 & ⇩*[des] L2 ≡ K2.
+#RR #RS #RP #Hacp #Hacr #L1 #K1 #des #H elim H -L1 -K1 -des
+[ /2 width=3/
+| #L1 #L #K1 #des #d #e #_ #HLK1 #IHL #K2 #HK12
+  elim (ldrop_lsubc_trans … Hacp Hacr … HLK1 … HK12) -Hacp -Hacr -K1 #K #HLK #HK2
+  elim (IHL … HLK) -IHL -HLK /3 width=5/
+]
+qed-.