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

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  14
  15 include "basic_2/multiple/fleq_fleq.ma".
  16 include "basic_2/reduction/fpbu_fleq.ma".
  17 include "basic_2/reduction/fpbc.ma".
  18
  19 (* "QRST" PROPER PARALLEL REDUCTION FOR CLOSURES ****************************)
  20
  21 (* Properties on lazy equivalence on closures *******************************)
  22
  23 lemma fpbc_fleq_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G, L, T⦄ →
  24                        ⦃G, L, T⦄ ≡[0] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄.
  25 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
  26 /3 width=9 by fleq_trans, ex2_3_intro/
  27 qed-.
  28
  29 lemma fleq_fpbc_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≡[0] ⦃G, L, T⦄ →
  30                        ⦃G, L, T⦄ ≻≡[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄.
  31 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 *
  32 #G0 #L0 #T0 #H0 #H02 elim (fleq_fpbu_trans … H1 … H0) -G -L -T
  33 /3 width=9 by fleq_trans, ex2_3_intro/
  34 qed-.