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15 include "basic_2/dynamic/lsubsv_lsstas.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
19 (* Properties on decomposed extended parallel computation on terms **********)
21 lemma lsubsv_cpds_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 •*➡*[h, g] T2 →
22 ∀L1. G ⊢ L1 ¡⊑[h, g] L2 →
23 ∃∃T. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g] T & ⦃G, L1⦄ ⊢ T2 ➡* T.
24 #h #g #G #L2 #T1 #T2 * #T #l1 #l2 #Hl21 #Hl1 #HT1 #HT2 #L1 #HL12
25 lapply (lsubsv_cprs_trans … HL12 … HT2) -HT2 #HT2
26 elim (lsubsv_lsstas_trans … HT1 … Hl1 … HL12) // #T0 #HT10 #HT0
27 lapply (lsubsv_fwd_lsubd … HL12) -HL12 #HL12
28 lapply (lsubd_da_trans … Hl1 … HL12) -L2 #Hl1
29 lapply (cpcs_cprs_strap1 … HT0 … HT2) -T #HT02
30 elim (cpcs_inv_cprs … HT02) -HT02 /3 width=7/