definition fpbc: ∀h. sd h → tri_relation genv lenv term ≝
λh,g,G1,L1,T1,G2,L2,T2.
- â\88\83â\88\83G,L,T. â¦\83G1, L1, T1â¦\84 â\89»[h, g] â¦\83G, L, Tâ¦\84 & â¦\83G, L, Tâ¦\84 â\8b\95[0] ⦃G2, L2, T2⦄.
+ â\88\83â\88\83G,L,T. â¦\83G1, L1, T1â¦\84 â\89»[h, g] â¦\83G, L, Tâ¦\84 & â¦\83G, L, Tâ¦\84 â\89¡[0] ⦃G2, L2, T2⦄.
interpretation
"single-step 'big tree' proper parallel reduction (closure)"
(* Baic properties **********************************************************)
lemma fpbu_fpbc: ∀h,g,G1,G2,L1,L2,T1,T2.
- â¦\83G1, L1, T1â¦\84 â\89»[h, g] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89»â\8b\95[h, g] ⦃G2, L2, T2⦄.
+ â¦\83G1, L1, T1â¦\84 â\89»[h, g] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89»â\89¡[h, g] ⦃G2, L2, T2⦄.
/2 width=5 by ex2_3_intro/ qed.