(* *)
(**************************************************************************)
-include "basic_2/s_computation/fqus.ma".
+include "static_2/s_computation/fqus.ma".
include "basic_2/rt_computation/fpbs.ma".
(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
(* Properties with star-iterated structural successor for closures **********)
-lemma fqus_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
- â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
+lemma fqus_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂* ❪G2,L2,T2❫ →
+ â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
/3 width=5 by fpbq_fquq, tri_step/
qed.
-lemma fpbs_fqus_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
- â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 â\8a\90* â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
+lemma fpbs_fqus_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
+ â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« â¬\82* â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
/3 width=5 by fpbs_strap1, fpbq_fquq/
qed-.
-lemma fqus_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
- â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\8a\90* â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqus_ind_dx … H) -G1 -L1 -T1
+lemma fqus_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫ →
+ â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« â¬\82* â\9dªG,L,Tâ\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
+#h #G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqus_ind_dx … H) -G1 -L1 -T1
/3 width=5 by fpbs_strap2, fpbq_fquq/
qed-.