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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2/equivalence/cpcs_cpcs.ma".
16 include "basic_2/dynamic/lsubsv.ma".
17
18 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
19
20 (* Properties on context-sensitive parallel equivalence for terms ***********)
21
22 lemma lsubsv_cpcs_trans: ∀h,o,G,L1,L2. G ⊢ L1 ⫃¡[h, o] L2 →
23                          ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ⬌* T2 → ⦃G, L1⦄ ⊢ T1 ⬌* T2.
24 /3 width=6 by lsubsv_fwd_lsubr, lsubr_cpcs_trans/
25 qed-.