-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/btsnalt_5.ma".
-include "basic_2/computation/fpbg_fpbs.ma".
-include "basic_2/computation/fsb.ma".
-
-(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
-
-(* Note: alternative definition of fsb *)
-inductive fsba (h) (o): relation3 genv lenv term ≝
-| fsba_intro: ∀G1,L1,T1. (
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄ → fsba h o G2 L2 T2
- ) → fsba h o G1 L1 T1.
-
-interpretation
- "'big tree' strong normalization (closure) alternative"
- 'BTSNAlt h o G L T = (fsba h o G L T).
-
-(* Basic eliminators ********************************************************)
-
-lemma fsba_ind_alt: ∀h,o. ∀R: relation3 …. (
- ∀G1,L1,T1. ⦥⦥[h,o] ⦃G1, L1, T1⦄ → (
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2
- ) → R G1 L1 T1
- ) →
- ∀G,L,T. ⦥⦥[h, o] ⦃G, L, T⦄ → R G L T.
-#h #o #R #IH #G #L #T #H elim H -G -L -T
-/4 width=1 by fsba_intro/
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma fsba_fpbs_trans: ∀h,o,G1,L1,T1. ⦥⦥[h, o] ⦃G1, L1, T1⦄ →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦥⦥[h, o] ⦃G2, L2, T2⦄.
-#h #o #G1 #L1 #T1 #H @(fsba_ind_alt … H) -G1 -L1 -T1
-/4 width=5 by fsba_intro, fpbs_fpbg_trans/
-qed-.
-
-(* Main properties **********************************************************)
-
-theorem fsb_fsba: ∀h,o,G,L,T. ⦥[h, o] ⦃G, L, T⦄ → ⦥⦥[h, o] ⦃G, L, T⦄.
-#h #o #G #L #T #H @(fsb_ind_alt … H) -G -L -T
-#G1 #L1 #T1 #_ #IH @fsba_intro
-#G2 #L2 #T2 * /3 width=5 by fsba_fpbs_trans/
-qed.
-
-(* Main inversion lemmas ****************************************************)
-
-theorem fsba_inv_fsb: ∀h,o,G,L,T. ⦥⦥[h, o] ⦃G, L, T⦄ → ⦥[h, o] ⦃G, L, T⦄.
-#h #o #G #L #T #H @(fsba_ind_alt … H) -G -L -T
-/4 width=1 by fsb_intro, fpb_fpbg/
-qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma fsb_fpbs_trans: ∀h,o,G1,L1,T1. ⦥[h, o] ⦃G1, L1, T1⦄ →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦥[h, o] ⦃G2, L2, T2⦄.
-/4 width=5 by fsba_inv_fsb, fsb_fsba, fsba_fpbs_trans/ qed-.
-
-(* Advanced eliminators *****************************************************)
-
-lemma fsb_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
- (∀G1,L1,T1. ⦥[h, o] ⦃G1, L1, T1⦄ →
- (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
- R G1 L1 T1
- ) →
- ∀G1,L1,T1. ⦥[h, o] ⦃G1, L1, T1⦄ → R G1 L1 T1.
-#h #o #R #IH #G1 #L1 #T1 #H @(fsba_ind_alt h o … G1 L1 T1)
-/3 width=1 by fsba_inv_fsb, fsb_fsba/
-qed-.