(* Properties with star-iterated structural successor for closures **********)
lemma fqus_fpbs:
- â\88\80G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82* â\9dªG2,L2,T2â\9d« →
- â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+ â\88\80G1,G2,L1,L2,T1,T2. â\9d¨G1,L1,T1â\9d© â¬\82* â\9d¨G2,L2,T2â\9d© →
+ â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
#G1 #G2 #L1 #L2 #T1 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
/3 width=5 by fquq_fpb, fpbs_strap1/
qed.
lemma fpbs_fqus_trans:
- â\88\80G1,G,L1,L,T1,T. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG,L,Tâ\9d« →
- 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¥ â\9dªG2,L2,T2â\9d«.
+ â\88\80G1,G,L1,L,T1,T. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G,L,Tâ\9d© →
+ â\88\80G2,L2,T2. â\9d¨G,L,Tâ\9d© â¬\82* â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
#G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqus_ind … H) -G2 -L2 -T2
/3 width=5 by fpbs_strap1, fquq_fpb/
qed-.
lemma fqus_fpbs_trans:
- â\88\80G,G2,L,L2,T,T2. â\9dªG,L,Tâ\9d« â\89¥ â\9dªG2,L2,T2â\9d« →
- 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¥ â\9dªG2,L2,T2â\9d«.
+ â\88\80G,G2,L,L2,T,T2. â\9d¨G,L,Tâ\9d© â\89¥ â\9d¨G2,L2,T2â\9d© →
+ â\88\80G1,L1,T1. â\9d¨G1,L1,T1â\9d© â¬\82* â\9d¨G,L,Tâ\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
#G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqus_ind_dx … H) -G1 -L1 -T1
/3 width=5 by fpbs_strap2, fquq_fpb/
qed-.