matita/matita/contribs/lambdadelta/basic_2A/computation/fpbs_fpb.ma

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  14
  15 include "basic_2A/reduction/fpbq_alt.ma".
  16 include "basic_2A/computation/fpbs_alt.ma".
  17
  18 (* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
  19
  20 (* Properties on extended context-sensitive parallel computation for terms **)
  21
  22 lemma fpbs_cpx_trans_neq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
  23                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, g] U2 → (T2 = U2 → ⊥) →
  24                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ≥[h, g] ⦃G2, L2, U2⦄.
  25 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 #HnTU2 elim (fpbs_inv_alt … H) -H
  26 #L00 #L0 #T0 #HT10 #H10 #HL00 #HL02 lapply (lleq_cpx_trans … HTU2 … HL02) -HTU2
  27 #HTU2 lapply (cpx_lleq_conf_sn … HTU2 … HL02) -HL02
  28 #HL02 lapply (lpxs_cpx_trans … HTU2 … HL00) -HTU2
  29 #HTU2 elim (fqus_cpxs_trans_neq … H10 … HTU2 HnTU2) -H10 -HTU2 -HnTU2
  30 #U0 #HTU0 #HnTU0 #HU02 elim (eq_term_dec T1 T0) #HnT10 destruct
  31 [ -HT10 elim (cpxs_neq_inv_step_sn … HTU0 HnTU0) -HTU0 -HnTU0
  32 | -HnTU0 elim (cpxs_neq_inv_step_sn … HT10 HnT10) -HT10 -HnT10
  33 ]
  34 /4 width=10 by fpbs_intro_alt, cpxs_trans, ex3_intro/
  35 qed-.
  36
  37 (* Properties on "rst" proper parallel reduction on closures ****************)
  38
  39 lemma fpb_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
  40                 ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
  41 /3 width=1 by fpbq_fpbs, fpb_fpbq/ qed.