matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_cpds.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/dynamic/lsubsv_lstas.ma".
  16
  17 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  18
  19 (* Properties on decomposed extended parallel computation on terms **********)
  20
  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_lstas_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 by ex2_intro, ex4_3_intro/
  31 qed-.