--- /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_2A/computation/lsubc_drop.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC REDUCIBILITY ********************)
+
+(* Properties concerning generic local environment slicing ******************)
+
+(* Basic_1: was: csubc_drop1_conf_rev *)
+lemma drops_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
+ ∀G,L1,K1,cs. ⬇*[Ⓕ, cs] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
+ ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇*[Ⓕ, cs] L2 ≡ K2.
+#RR #RS #RP #Hgcp #G #L1 #K1 #cs #H elim H -L1 -K1 -cs
+[ /2 width=3 by drops_nil, ex2_intro/
+| #L1 #L #K1 #cs #l #m #_ #HLK1 #IHL #K2 #HK12
+ elim (drop_lsubc_trans … Hgcp … HLK1 … HK12) -Hgcp -K1 #K #HLK #HK2
+ elim (IHL … HLK) -IHL -HLK /3 width=5 by drops_cons, ex2_intro/
+]
+qed-.