(* Properties on decomposed extended parallel computation on terms **********)
lemma lsubsv_cpds_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 •*➡*[h, g] T2 →
- ∀L1. G ⊢ L1 ¡⫃[h, g] L2 →
+ ∀L1. G ⊢ L1 ⫃¡[h, g] L2 →
∃∃T. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g] T & ⦃G, L1⦄ ⊢ T2 ➡* T.
#h #g #G #L2 #T1 #T2 * #T #l1 #l2 #Hl21 #Hl1 #HT1 #HT2 #L1 #HL12
lapply (lsubsv_cprs_trans … HL12 … HT2) -HT2 #HT2