(**************************************************************************)
include "basic_2/notation/relations/btsn_5.ma".
-include "basic_2/reduction/fpbc.ma".
+include "basic_2/reduction/fpb.ma".
include "basic_2/computation/csx.ma".
-(* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
+(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
inductive fsb (h) (g): relation3 genv lenv term ≝
| fsb_intro: ∀G1,L1,T1. (
.
interpretation
- "'big tree' strong normalization (closure)"
+ "'qrst' strong normalization (closure)"
'BTSN h g G L T = (fsb h g G L T).
(* Basic eliminators ********************************************************)
-theorem fsb_ind_alt: ∀h,g. ∀R: relation3 …. (
- ∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⦥[h,g] T1 → (
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
- (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄ → ⊥) → R G2 L2 T2
- ) → R G1 L1 T1
- ) →
- ∀G,L,T. ⦃G, L⦄ ⊢ ⦥[h, g] T → R G L T.
+lemma fsb_ind_alt: ∀h,g. ∀R: relation3 …. (
+ ∀G1,L1,T1. ⦥[h,g] ⦃G1, L1, T1⦄ → (
+ ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2
+ ) → R G1 L1 T1
+ ) →
+ ∀G,L,T. ⦥[h, g] ⦃G, L, T⦄ → R G L T.
#h #g #R #IH #G #L #T #H elim H -G -L -T
-/5 width=1 by fpb_fpbc, fsb_intro/
+/4 width=1 by fsb_intro/
qed-.
(* Basic inversion lemmas ***************************************************)
-lemma fsb_inv_csx: â\88\80h,g,G,L,T. â¦\83G, Lâ¦\84 â\8a¢ ⦥[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpbc_cpx/
+lemma fsb_inv_csx: â\88\80h,g,G,L,T. ⦥[h, g] â¦\83G, L, Tâ¦\84 → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
+#h #g #G #L #T #H elim H -G -L -T /5 width=1 by csx_intro, fpb_cpx/
qed-.