(**************************************************************************)
include "basic_2/notation/relations/btpred_8.ma".
-include "basic_2/relocation/fsup.ma".
-include "basic_2/static/ssta.ma".
-include "basic_2/reduction/lpr.ma".
+include "basic_2/relocation/fquq.ma".
+include "basic_2/substitution/lleq.ma".
+include "basic_2/reduction/lpx.ma".
(* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
inductive fpb (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpb_fsup : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
-| fpb_lpr : ∀L2. ⦃G1, L1⦄ ⊢ ➡ L2 → fpb h g G1 L1 T1 G1 L2 T1
-| fpb_cpr : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → fpb h g G1 L1 T1 G1 L1 T2
-| fpb_ssta : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
+| fpb_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpb h g G1 L1 T1 G2 L2 T2
+| fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡[h, g] T2 → fpb h g G1 L1 T1 G1 L1 T2
+| fpb_lpx : ∀L2. ⦃G1, L1⦄ ⊢ ➡[h, g] L2 → fpb h g G1 L1 T1 G1 L2 T1
+| fpb_lleq: ∀L2. L1 ⋕[T1, 0] L2 → fpb h g G1 L1 T1 G1 L2 T1
.
interpretation
(* Basic properties *********************************************************)
lemma fpb_refl: ∀h,g. tri_reflexive … (fpb h g).
-/2 width=1 by fpb_cpr/ qed.
+/2 width=1 by fpb_cpx/ qed.
+
+lemma cpr_fpb: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L, T1⦄ ≽[h, g] ⦃G, L, T2⦄.
+/3 width=1 by fpb_cpx, cpr_cpx/ qed.
+
+lemma lpr_fpb: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1, T⦄ ≽[h, g] ⦃G, L2, T⦄.
+/3 width=1 by fpb_lpx, lpr_lpx/ qed.