(**************************************************************************)
include "basic_2/notation/relations/lazybtpredproper_8.ma".
-include "basic_2/computation/fpns.ma".
+include "basic_2/substitution/fleq.ma".
include "basic_2/computation/fpbu.ma".
(* SINGLE-STEP "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********)
definition fpbc: ∀h. sd h → tri_relation genv lenv term ≝
λh,g,G1,L1,T1,G2,L2,T2.
- ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ .
+ ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≡[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.