definition fpbsa: ∀h. sd h → tri_relation genv lenv term ≝
λh,g,G1,L1,T1,G2,L2,T2.
∃∃L0,L,T. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T &
- â¦\83G1, L1, Tâ¦\84 â\8a\83* ⦃G2, L0, T2⦄ &
- â¦\83G2, L0â¦\84 â\8a¢ â\9e¡*[h, g] L & L â\8b\95[T2, 0] L2.
+ â¦\83G1, L1, Tâ¦\84 â\8a\90* ⦃G2, L0, T2⦄ &
+ â¦\83G2, L0â¦\84 â\8a¢ â\9e¡*[h, g] L & L â\89¡[T2, 0] L2.
interpretation "'big tree' parallel computation (closure) alternative"
'BTPRedStarAlt h g G1 L1 T1 G2 L2 T2 = (fpbsa h g G1 L1 T1 G2 L2 T2).
(* Advanced properties ******************************************************)
lemma fpbs_intro_alt: ∀h,g,G1,G2,L1,L0,L,L2,T1,T,T2.
- â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, g] T â\86\92 â¦\83G1, L1, Tâ¦\84 â\8a\83* ⦃G2, L0, T2⦄ →
- â¦\83G2, L0â¦\84 â\8a¢ â\9e¡*[h, g] L â\86\92 L â\8b\95[T2, 0] L2 → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ .
+ â¦\83G1, L1â¦\84 â\8a¢ T1 â\9e¡*[h, g] T â\86\92 â¦\83G1, L1, Tâ¦\84 â\8a\90* ⦃G2, L0, T2⦄ →
+ â¦\83G2, L0â¦\84 â\8a¢ â\9e¡*[h, g] L â\86\92 L â\89¡[T2, 0] L2 → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ .
/3 width=7 by fpbsa_inv_fpbs, ex4_3_intro/ qed.
(* Advanced inversion lemmas *************************************************)
lemma fpbs_inv_alt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
∃∃L0,L,T. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] T &
- â¦\83G1, L1, Tâ¦\84 â\8a\83* ⦃G2, L0, T2⦄ &
- â¦\83G2, L0â¦\84 â\8a¢ â\9e¡*[h, g] L & L â\8b\95[T2, 0] L2.
+ â¦\83G1, L1, Tâ¦\84 â\8a\90* ⦃G2, L0, T2⦄ &
+ â¦\83G2, L0â¦\84 â\8a¢ â\9e¡*[h, g] L & L â\89¡[T2, 0] L2.
/2 width=1 by fpbs_fpbsa/ qed-.