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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-.