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15 include "basic_2/reduction/fpbc_fleq.ma".
16 include "basic_2/computation/fpbg.ma".
18 (* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
20 (* Properties on lazy equivalence for closures ******************************)
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/
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/