(* Properties with star-iterated structural successor for closures **********)
-lemma fqus_lpxs_fpbs: â\88\80h,G1,G2,L1,L,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90* ⦃G2,L,T2⦄ →
+lemma fqus_lpxs_fpbs: â\88\80h,G1,G2,L1,L,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82* ⦃G2,L,T2⦄ →
∀L2. ⦃G2,L⦄ ⊢ ⬈*[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
/3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed.
(* Properties with unbound context-sensitive parallel rt-computation ********)
lemma cpxs_fqus_lpxs_fpbs: ∀h,G1,L1,T1,T. ⦃G1,L1⦄ ⊢ T1 ⬈*[h] T →
- â\88\80G2,L,T2. â¦\83G1,L1,Tâ¦\84 â\8a\90* ⦃G2,L,T2⦄ →
+ â\88\80G2,L,T2. â¦\83G1,L1,Tâ¦\84 â¬\82* ⦃G2,L,T2⦄ →
∀L2.⦃G2,L⦄ ⊢ ⬈*[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
/3 width=5 by cpxs_fqus_fpbs, fpbs_lpxs_trans/ qed.
lemma fpbs_cpxs_tdeq_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ⦃G1,L1,T1⦄ ≥ [h] ⦃G3,L3,T3⦄ →
∀T4. ⦃G3,L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
- â\88\80G2,L4,T2. â¦\83G3,L3,T5â¦\84 â\8a\90+ ⦃G2,L4,T2⦄ →
+ â\88\80G2,L4,T2. â¦\83G3,L3,T5â¦\84 â¬\82+ ⦃G2,L4,T2⦄ →
∀L2. ⦃G2,L4⦄ ⊢ ⬈[h] L2 → ⦃G1,L1,T1⦄ ≥ [h] ⦃G2,L2,T2⦄.
#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42
@(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *)
(* Basic_2A1: uses: fpbs_intro_alt *)
lemma fpbs_intro_star: ∀h,G1,L1,T1,T. ⦃G1,L1⦄ ⊢ T1 ⬈*[h] T →
- â\88\80G,L,T0. â¦\83G1,L1,Tâ¦\84 â\8a\90* ⦃G,L,T0⦄ →
+ â\88\80G,L,T0. â¦\83G1,L1,Tâ¦\84 â¬\82* ⦃G,L,T0⦄ →
∀L0. ⦃G,L⦄ ⊢ ⬈*[h] L0 →
∀G2,L2,T2. ⦃G,L0,T0⦄ ≛ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ .
/3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_fdeq/ qed.
(* Basic_2A1: uses: fpbs_inv_alt *)
lemma fpbs_inv_star: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ →
- â\88\83â\88\83G,L,L0,T,T0. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] T & â¦\83G1,L1,Tâ¦\84 â\8a\90* ⦃G,L,T0⦄
+ â\88\83â\88\83G,L,L0,T,T0. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] T & â¦\83G1,L1,Tâ¦\84 â¬\82* ⦃G,L,T0⦄
& ⦃G,L⦄ ⊢ ⬈*[h] L0 & ⦃G,L0,T0⦄ ≛ ⦃G2,L2,T2⦄.
#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
[ /2 width=9 by ex4_5_intro/