(* Advanced properties ******************************************************)
lemma teqx_fpbs_trans: ∀h,T1,T. T1 ≛ T →
- â\88\80G1,G2,L1,L2,T2. â¦\83G1,L1,Tâ¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+ â\88\80G1,G2,L1,L2,T2. â\9dªG1,L1,Tâ\9d« â\89¥[h] â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
/3 width=5 by feqx_fpbs_trans, teqx_feqx/ qed-.
-lemma fpbs_teqx_trans: â\88\80h,G1,G2,L1,L2,T1,T. â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,Tâ¦\84 →
- â\88\80T2. T â\89\9b T2 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma fpbs_teqx_trans: â\88\80h,G1,G2,L1,L2,T1,T. â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,Tâ\9d« →
+ â\88\80T2. T â\89\9b T2 â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
/3 width=5 by fpbs_feqx_trans, teqx_feqx/ qed-.
(* Properties with plus-iterated structural successor for closures **********)
-lemma fqup_fpbs: â\88\80h,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82+ â¦\83G2,L2,T2â¦\84 →
- â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma fqup_fpbs: â\88\80h,G1,G2,L1,L2,T1,T2. â\9dªG1,L1,T1â\9d« â¬\82+ â\9dªG2,L2,T2â\9d« →
+ â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
/4 width=5 by fqu_fquq, fpbq_fquq, tri_step/
qed.
-lemma fpbs_fqup_trans: â\88\80h,G1,G,L1,L,T1,T. â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G,L,Tâ¦\84 →
- â\88\80G2,L2,T2. â¦\83G,L,Tâ¦\84 â¬\82+ â¦\83G2,L2,T2â¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma fpbs_fqup_trans: â\88\80h,G1,G,L1,L,T1,T. â\9dªG1,L1,T1â\9d« â\89¥[h] 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¥[h] â\9dªG2,L2,T2â\9d«.
/3 width=5 by fpbs_fqus_trans, fqup_fqus/ qed-.
-lemma fqup_fpbs_trans: â\88\80h,G,G2,L,L2,T,T2. â¦\83G,L,Tâ¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84 →
- â\88\80G1,L1,T1. â¦\83G1,L1,T1â¦\84 â¬\82+ â¦\83G,L,Tâ¦\84 â\86\92 â¦\83G1,L1,T1â¦\84 â\89¥[h] â¦\83G2,L2,T2â¦\84.
+lemma fqup_fpbs_trans: â\88\80h,G,G2,L,L2,T,T2. â\9dªG,L,Tâ\9d« â\89¥[h] 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¥[h] â\9dªG2,L2,T2â\9d«.
/3 width=5 by fqus_fpbs_trans, fqup_fqus/ qed-.