matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_ext.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  14
  15 include "basic_2/computation/fpbs_alt.ma".
  16
  17 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
  18
  19 (* Properties on extended context-sensitive parallel computation for terms **)
  20
  21 lemma fpbs_cpxs_trans_neq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
  22                            ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 → (T2 = U2 → ⊥) →
  23                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ≥[h, g] ⦃G2, L2, U2⦄.
  24 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 #HnTU2 elim (fpbs_inv_alt … H) -H
  25 #L00 #L0 #T0 #HT10 #H10 #HL00 #HL02 lapply (lleq_cpxs_trans … HTU2 … HL02) -HTU2
  26 #HTU2 lapply (cpxs_lleq_conf_sn … HTU2 … HL02) -HL02
  27 #HL02 lapply (lpxs_cpxs_trans … HTU2 … HL00) -HTU2
  28 #HTU2 elim (fqus_cpxs_trans_neq … H10 … HTU2 HnTU2) -H10 -HTU2 -HnTU2
  29 #U0 #HTU0 #HnTU0 #HU02 elim (eq_term_dec T1 T0) [ -HT10 | -HnTU0 ]
  30 [ #H destruct ] /3 width=10 by fpbs_intro_alt, ex3_intro/
  31 qed-.