(* Properties with star-iterated structural successor for closures **********)
lemma fdeq_fqus_trans: ∀b,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ≛ ⦃G,L,T⦄ →
- â\88\80G2,L2,T2. â¦\83G,L,Tâ¦\84 â\8a\90*[b] ⦃G2,L2,T2⦄ →
- â\88\83â\88\83G,L0,T0. â¦\83G1,L1,T1â¦\84 â\8a\90*[b] ⦃G,L0,T0⦄ & ⦃G,L0,T0⦄ ≛ ⦃G2,L2,T2⦄.
+ â\88\80G2,L2,T2. â¦\83G,L,Tâ¦\84 â¬\82*[b] ⦃G2,L2,T2⦄ →
+ â\88\83â\88\83G,L0,T0. â¦\83G1,L1,T1â¦\84 â¬\82*[b] ⦃G,L0,T0⦄ & ⦃G,L0,T0⦄ ≛ ⦃G2,L2,T2⦄.
#b #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H2
elim(fdeq_inv_gen_dx … H1) -H1 #HG #HL1 #HT1 destruct
elim (rdeq_fqus_trans … H2 … HL1) -L #L #T0 #H2 #HT02 #HL2