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14
15 include "ground/lib/star.ma".
16 include "basic_2/notation/relations/predsubtystar_6.ma".
17 include "basic_2/rt_transition/fpb.ma".
18
19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
20
21 definition fpbs: tri_relation genv lenv term ≝
22            tri_TC … fpb.
23
24 interpretation
25   "parallel rst-computation (closure)"
26   'PRedSubTyStar  G1 L1 T1 G2 L2 T2 = (fpbs G1 L1 T1 G2 L2 T2).
27
28
29 (* Basic properties *********************************************************)
30
31 (* Basic_2A1: uses: fpbq_fpbs *)
32 lemma fpb_fpbs:
33       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
34       ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
35 /2 width=1 by tri_inj/ qed.
36
37 lemma fpbs_strap1:
38       ∀G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
39       ❪G,L,T❫ ≽ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
40 /2 width=5 by tri_step/ qed-.
41
42 lemma fpbs_strap2:
43       ∀G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≽ ❪G,L,T❫ →
44       ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
45 /2 width=5 by tri_TC_strap/ qed-.
46
47 (* Basic_2A1: removed theorems 3:
48               fpb_fpbsa_trans fpbs_fpbsa fpbsa_inv_fpbs
49 *)