(* *)
(**************************************************************************)
+include "basic_2/static/lsubd_da.ma".
+include "basic_2/dynamic/lsubsv_lsubd.ma".
include "basic_2/dynamic/lsubsv_lstas.ma".
(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
(* Properties on decomposed extended parallel computation on terms **********)
-lemma lsubsv_scpds_trans: ∀h,g,G,L2,T1,T2,l. ⦃G, L2⦄ ⊢ T1 •*➡*[h, g, l] T2 →
- ∀L1. G ⊢ L1 ⫃¡[h, g] L2 →
- ∃∃T. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g, l] T & ⦃G, L1⦄ ⊢ T2 ➡* T.
-#h #g #G #L2 #T1 #T2 #l2 * #T #l1 #Hl21 #Hl1 #HT1 #HT2 #L1 #HL12
+lemma lsubsv_scpds_trans: ∀h,o,G,L2,T1,T2,d. ⦃G, L2⦄ ⊢ T1 •*➡*[h, o, d] T2 →
+ ∀L1. G ⊢ L1 ⫃¡[h, o] L2 →
+ ∃∃T. ⦃G, L1⦄ ⊢ T1 •*➡*[h, o, d] T & ⦃G, L1⦄ ⊢ T2 ➡* T.
+#h #o #G #L2 #T1 #T2 #d2 * #T #d1 #Hd21 #Hd1 #HT1 #HT2 #L1 #HL12
lapply (lsubsv_cprs_trans … HL12 … HT2) -HT2 #HT2
-elim (lsubsv_lstas_trans … HT1 … Hl1 … HL12) // #T0 #HT10 #HT0
+elim (lsubsv_lstas_trans … HT1 … Hd1 … HL12) // #T0 #HT10 #HT0
lapply (cpcs_cprs_strap1 … HT0 … HT2) -T #HT02
elim (cpcs_inv_cprs … HT02) -HT02
/5 width=5 by lsubsv_fwd_lsubd, lsubd_da_trans, ex4_2_intro, ex2_intro/