matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma

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  14
  15 include "basic_2/rt_computation/fpbs_fpbs.ma".
  16 include "basic_2/rt_computation/fpbg.ma".
  17
  18 (* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
  19
  20 (* Advanced forward lemmas **************************************************)
  21
  22 lemma fpbg_fwd_fpbs (G1) (G2) (L1) (L2) (T1) (T2):
  23       ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
  24 #G1 #G2 #L1 #L2 #T1 #T2 #H
  25 elim (fpbg_inv_gen … H) -H
  26 /4 width=9 by fpbs_trans, fpbs_strap2, fpbc_fwd_fpb/
  27 qed-.
  28
  29 (* Advanced properties ******************************************************)
  30
  31 lemma fpbs_fpbg_trans (G) (L) (T):
  32       ∀G1,L1,T1. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
  33       ∀G2,L2,T2. ❪G,L,T❫ > ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
  34 #G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
  35 elim (fpbg_inv_gen … H2) -H2
  36 /3 width=13 by fpbg_intro, fpbs_trans/
  37 qed-.
  38
  39 (* Note: this is used in the closure proof *)
  40 lemma fpbg_fpbs_trans (G) (L) (T):
  41       ∀G1,L1,T1. ❪G1,L1,T1❫ > ❪G,L,T❫ →
  42       ∀G2,L2,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
  43 #G #L #T #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
  44 elim (fpbg_inv_gen … H1) -H1
  45 /3 width=13 by fpbg_intro, fpbs_trans/
  46 qed-.