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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/static/lsubd_da.ma".
16 include "basic_2/dynamic/lsubsv_lsubd.ma".
17 include "basic_2/dynamic/lsubsv_lstas.ma".
19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
21 (* Properties on decomposed extended parallel computation on terms **********)
23 lemma lsubsv_scpds_trans: ∀h,g,G,L2,T1,T2,l. ⦃G, L2⦄ ⊢ T1 •*➡*[h, g, l] T2 →
24 ∀L1. G ⊢ L1 ⫃¡[h, g] L2 →
25 ∃∃T. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g, l] T & ⦃G, L1⦄ ⊢ T2 ➡* T.
26 #h #g #G #L2 #T1 #T2 #l2 * #T #l1 #Hl21 #Hl1 #HT1 #HT2 #L1 #HL12
27 lapply (lsubsv_cprs_trans … HL12 … HT2) -HT2 #HT2
28 elim (lsubsv_lstas_trans … HT1 … Hl1 … HL12) // #T0 #HT10 #HT0
29 lapply (cpcs_cprs_strap1 … HT0 … HT2) -T #HT02
30 elim (cpcs_inv_cprs … HT02) -HT02
31 /5 width=5 by lsubsv_fwd_lsubd, lsubd_da_trans, ex4_2_intro, ex2_intro/