matita/matita/contribs/lambdadelta/basic_2A/etc/fpbc/fpbg_fleq.etc

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  14
  15 include "basic_2/reduction/fpbc_fleq.ma".
  16 include "basic_2/computation/fpbg.ma".
  17
  18 (* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
  19
  20 (* Properties on lazy equivalence for closures ******************************)
  21
  22 lemma fpbg_fleq_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ →
  23                        ∀G2,L2,T2. ⦃G, L, T⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
  24 #h #g #G1 #G #L1 #L #T1 #T #H @(fpbg_ind … H) -G -L -T
  25 [ /3 width=5 by fpbc_fpbg, fpbc_fleq_trans/
  26 | /4 width=9 by fpbg_strap1, fpbc_fleq_trans/
  27 ]
  28 qed-.
  29
  30 lemma fleq_fpbg_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
  31                        ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≡[0] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
  32 #h #g #G #G2 #L #L2 #T #T2 #H @(fpbg_ind_dx … H) -G -L -T
  33 [ /3 width=5 by fpbc_fpbg, fleq_fpbc_trans/
  34 | /4 width=9 by fpbg_strap2, fleq_fpbc_trans/
  35 ]
  36 qed-.