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15 include "static_2/static/feqg_fqup.ma".
16 include "basic_2/rt_transition/fpbc_feqg.ma".
17 include "basic_2/rt_computation/fsb.ma".
19 (* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
21 (* Properties with generic equivalence for closures *************************)
23 lemma fsb_feqg_trans (S):
24 reflexive … S → symmetric … S → Transitive … S →
25 ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
26 ∀G2,L2,T2. ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫.
27 #S #H1S #H2S #H3S #G1 #L1 #T1 #H @(fsb_ind … H) -G1 -L1 -T1
28 #G1 #L1 #T1 #_ #IH #G2 #L2 #T2 #H12
29 @fsb_intro #G #L #T #H2
30 elim (feqg_fpbc_trans … H12 … H2) -G2 -L2 -T2
31 /4 width=5 by fpbc_intro, feqg_refl/