(* *)
(**************************************************************************)
-include "basic_2/rt_computation/fpbg_fpbs.ma".
+include "basic_2/rt_computation/fpbg_fqup.ma".
+include "basic_2/rt_computation/fpbg_feqg.ma".
include "basic_2/rt_computation/fsb_feqg.ma".
(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
#G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
elim (fpbs_inv_fpbg … H12) -H12
[ -IH /2 width=9 by fsb_feqg_trans/
-| -H1 * /2 width=5 by/
+| -H1 #H elim (fpbg_inv_fpbc_fpbs … H)
+ /2 width=5 by/
]
qed-.
+(* Properties with parallel rst-transition for closures *********************)
+
+lemma fsb_fpb_trans:
+ ∀G1,L1,T1. ≥𝐒 ❪G1,L1,T1❫ →
+ ∀G2,L2,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫.
+/3 width=5 by fsb_fpbs_trans, fpb_fpbs/ qed-.
+
(* Properties with proper parallel rst-computation for closures *************)
lemma fsb_intro_fpbg:
∀G1,L1,T1.
(∀G2,L2,T2. ❪G1,L1,T1❫ > ❪G2,L2,T2❫ → ≥𝐒 ❪G2,L2,T2❫) →
≥𝐒 ❪G1,L1,T1❫.
-/4 width=1 by fsb_intro, fpb_fpbg/ qed.
+/4 width=1 by fsb_intro, fpbc_fpbg/ qed.
(* Eliminators with proper parallel rst-computation for closures ************)
@IH1 -IH1
[ -IH /2 width=5 by fsb_fpbs_trans/
| -H1 #G0 #L0 #T0 #H10
- elim (fpbs_fpbg_trans … H12 … H10) -G2 -L2 -T2
+ lapply (fpbs_fpbg_trans … H12 … H10) -G2 -L2 -T2 #H
+ elim (fpbg_inv_fpbc_fpbs … H) -H #G #L #T #H1 #H0
/2 width=5 by/
]
qed-.