--- /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/rdeq_fqus.ma".
+include "static_2/static/fdeq.ma".
+
+(* DEGREE-BASED EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES ****************)
+
+(* Properties with star-iterated structural successor for closures **********)
+
+lemma fdeq_fqus_trans: ∀h,o,b,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≛[h, o] ⦃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⦄ ≛[h, o] ⦃G2, L2, T2⦄.
+#h #o #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
+elim (tdeq_fqus_trans … H2 … HT1) -T #L0 #T #H2 #HT0 #HL0
+lapply (tdeq_rdeq_conf … HT02 … HL0) -HL0 #HL0
+/4 width=7 by fdeq_intro_dx, rdeq_trans, tdeq_trans, ex2_3_intro/
+qed-.