matita/matita/contribs/lambdadelta/basic_2/etc/fpb/fpb_fleq.etc

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  14
  15 include "basic_2/multiple/fleq.ma".
  16 include "basic_2/reduction/fpb_lleq.ma".
  17
  18 (* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
  19
  20 (* Properties on lazy equivalence for closures ******************************)
  21
  22 lemma fleq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≡[0] ⦃F2, K2, T2⦄ →
  23                       ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
  24                       ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≡[0] ⦃G2, L2, U2⦄.
  25 #h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
  26 #K2 #HK12 #G2 #L2 #U2 #H12 elim (lleq_fpb_trans … HK12 … H12) -K2
  27 /3 width=5 by fleq_intro, ex2_3_intro/
  28 qed-.
  29
  30 (* Inversion lemmas on lazy equivalence for closures ************************)
  31
  32 lemma fpb_inv_fleq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
  33                     ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥.
  34 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  35 [ #G2 #L2 #T2 #H12 #H elim (fleq_inv_gen … H) -H
  36   /3 width=8 by lleq_fwd_length, fqu_inv_eq/
  37 | #T2 #_ #HnT #H elim (fleq_inv_gen … H) -H /2 width=1 by/
  38 | #L2 #_ #HnL #H elim (fleq_inv_gen … H) -H /2 width=1 by/
  39 ]
  40 qed-.
  41