(* Properties with star-iterated structural successor for closures **********)
-lemma fqus_fpbs: â\88\80h,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90* ⦃G2,L2,T2⦄ →
+lemma fqus_fpbs: â\88\80h,G1,G2,L1,L2,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82* ⦃G2,L2,T2⦄ →
⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
#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,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G,L,T⦄ →
- â\88\80G2,L2,T2. â¦\83G,L,Tâ¦\84 â\8a\90* ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
+ â\88\80G2,L2,T2. â¦\83G,L,Tâ¦\84 â¬\82* ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
#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,G,G2,L,L2,T,T2. ⦃G,L,T⦄ ≥[h] ⦃G2,L2,T2⦄ →
- â\88\80G1,L1,T1. â¦\83G1,L1,T1â¦\84 â\8a\90* ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
+ â\88\80G1,L1,T1. â¦\83G1,L1,T1â¦\84 â¬\82* ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
#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-.