(* *)
(**************************************************************************)
-include "basic_2/computation/lpxs_ffdeq.ma".
-include "basic_2/computation/fpbg_ffdeq.ma".
+include "basic_2/rt_computation/fpbs_lfpxs.ma".
+include "basic_2/rt_computation/fpbg.ma".
-(* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES **************************)
+(* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
-lemma lpxs_fpbg: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡*[h, o] L2 →
- (L1 ≡[T, 0] L2 → ⊥) → ⦃G, L1, T⦄ >≛[h, o] ⦃G, L2, T⦄.
-#h #o #G #L1 #L2 #T #H #H0 elim (lpxs_nlleq_inv_step_sn … H … H0) -H -H0
-/4 width=5 by fpb_lpx, lpxs_lleq_fpbs, ex2_3_intro/
+(* Properties with uncounted parallel rt-computation on referred entries ****)
+
+(* Basic_2A1: uses: lpxs_fpbg *)
+lemma lfpxs_lfdneq_fpbg: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 →
+ (L1 ≛[h, o, T] L2 → ⊥) → ⦃G, L1, T⦄ >[h, o] ⦃G, L2, T⦄.
+#h #o #G #L1 #L2 #T #H #H0
+elim (lfpxs_lfdneq_inv_step_sn … H … H0) -H -H0
+/4 width=7 by fpb_lfpx, lfpxs_ffdeq_fpbs, ffdeq_intro_sn, ex2_3_intro/
qed.
(* *)
(**************************************************************************)
-include "basic_2/static/ffdeq_fqup.ma".
include "basic_2/static/ffdeq_fqus.ma".
include "basic_2/static/ffdeq_ffdeq.ma".
include "basic_2/rt_computation/cpxs_fqus.ma".
qed-.
(* Basic_2A1: uses: lpxs_lleq_fpbs *)
-lemma lpxs_ffdeq_fpbs: ∀h,o,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, T1] L →
- ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma lfpxs_ffdeq_fpbs: ∀h,o,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, T1] L →
+ ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
/3 width=3 by lfpxs_fpbs_trans, ffdeq_fpbs/ qed.
(* Properties with star-iterated structural successor for closures **********)
lfsx.ma lfsx_drops.ma lfsx_fqup.ma lfsx_lpx.ma lfsx_lpxs.ma lfsx_lfpxs.ma lfsx_csx.ma lfsx_lfsx.ma
lsubsx.ma lsubsx_lfsx.ma lsubsx_lsubsx.ma
fpbs.ma fpbs_fqup.ma fpbs_fqus.ma fpbs_aaa.ma fpbs_fpb.ma fpbs_cpxs.ma fpbs_lfpxs.ma fpbs_csx.ma fpbs_fpbs.ma
-fpbg.ma fpbg_fqup.ma fpbg_cpxs.ma fpbg_fpbs.ma fpbg_fpbg.ma
+fpbg.ma fpbg_fqup.ma fpbg_cpxs.ma fpbg_lfpxs.ma fpbg_fpbs.ma fpbg_fpbg.ma
]
*)
[ { "uncounted context-sensitive parallel rst-computation" * } {
- [ [ "proper for closures" ] "fpbg" + "( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "fpbg_fqup" + "fpbg_cpxs" + "fpbg_fpbs" + "fpbg_fpbg" * ]
+ [ [ "proper for closures" ] "fpbg" + "( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "fpbg_fqup" + "fpbg_cpxs" + "fpbg_lfpxs" + "fpbg_fpbs" + "fpbg_fpbg" * ]
[ [ "for closures" ] "fpbs" + "( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_fqup" + "fpbs_fqus" + "fpbs_aaa" + "fpbs_fpb" + "fpbs_cpxs" + "fpbs_lfpxs" + "fpbs_csx" + "fpbs_fpbs" * ]
}
]