--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "static_2/static/reqg_fqus.ma".
+include "static_2/static/feqg.ma".
+
+(* GENERIC EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *********************)
+
+(* Properties with star-iterated structural successor for closures **********)
+
+lemma feqg_fqus_trans (S) (b):
+ reflexive … S → symmetric … S → Transitive … S →
+ ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≛[S] ❪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❫ ≛[S] ❪G2,L2,T2❫.
+#S #b #H1S #H2S #H3S #G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H2
+elim(feqg_inv_gen_dx … H1) -H1 // #HG #HL1 #HT1 destruct
+elim (reqg_fqus_trans … H2 … HL1) -L // #L #T0 #H2 #HT02 #HL2
+elim (teqg_fqus_trans … H2 … HT1) -T // #L0 #T #H2 #HT0 #HL0
+lapply (teqg_reqg_conf_sn … HT02 … HL0) -HL0 // #HL0
+/4 width=7 by feqg_intro_dx, reqg_trans, teqg_trans, ex2_3_intro/
+qed-.