(* Properties with star-iterated structural successor for closures **********)
-lemma feqx_fqus_trans: ∀b,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛ ❪G,L,T❫ →
- ∀G2,L2,T2. ❪G,L,T❫ ⬂*[b] ❪G2,L2,T2❫ →
- ∃∃G,L0,T0. ❪G1,L1,T1❫ ⬂*[b] ❪G,L0,T0❫ & ❪G,L0,T0❫ ≛ ❪G2,L2,T2❫.
+lemma feqx_fqus_trans (b):
+ ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛ ❪G,L,T❫ →
+ ∀G2,L2,T2. ❪G,L,T❫ ⬂*[b] ❪G2,L2,T2❫ →
+ ∃∃G,L0,T0. ❪G1,L1,T1❫ ⬂*[b] ❪G,L0,T0❫ & ❪G,L0,T0❫ ≛ ❪G2,L2,T2❫.
#b #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H2
elim(feqx_inv_gen_dx … H1) -H1 #HG #HL1 #HT1 destruct
elim (reqx_fqus_trans … H2 … HL1) -L #L #T0 #H2 #HT02 #HL2
elim (teqx_fqus_trans … H2 … HT1) -T #L0 #T #H2 #HT0 #HL0
-lapply (teqx_reqx_conf … HT02 … HL0) -HL0 #HL0
+lapply (teqx_reqx_conf_sn … HT02 … HL0) -HL0 #HL0
/4 width=7 by feqx_intro_dx, reqx_trans, teqx_trans, ex2_3_intro/
qed-.