(**************************************************************************) (* ___ *) (* ||M|| *) (* ||A|| A project by Andrea Asperti *) (* ||T|| *) (* ||I|| Developers: *) (* ||T|| The HELM team. *) (* ||A|| http://helm.cs.unibo.it *) (* \ / *) (* \ / This file is distributed under the terms of the *) (* v GNU General Public License Version 2 *) (* *) (**************************************************************************) include "basic_2/dynamic/lsubsv_lsstas.ma". (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************) (* 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 → ∃∃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 elim (lsubsv_lsstas_trans … HT1 … Hl1 … HL12) // #T0 #HT10 #HT0 lapply (lsubsv_fwd_lsubd … HL12) -HL12 #HL12 lapply (lsubd_da_trans … Hl1 … HL12) -L2 #Hl1 lapply (cpcs_cprs_strap1 … HT0 … HT2) -T #HT02 elim (cpcs_inv_cprs … HT02) -HT02 /3 width=7/ qed-.