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diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_eq.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_eq.ma
new file mode 100644
index 000000000..0d569e6df
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr_eq.ma
@@ -0,0 +1,36 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
+
+include "delayed_updating/reduction/ibfr.ma".
+include "delayed_updating/substitution/fsubst_eq.ma".
+include "delayed_updating/substitution/lift_prototerm_eq.ma".
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma ibfr_eq_canc_sn (t) (t1) (t2) (r):
+      t ⇔ t1 → t ➡𝐢𝐛𝐟[r] t2 → t1 ➡𝐢𝐛𝐟[r] t2.
+#t #t1 #t2 #r #Ht1
+* #p #b #q #m #n #Hr#Hp #Hb #Hm #Hn #Ht #Ht2 destruct
+@(ex7_5_intro … Hp Hb Hm Hn) [ // ] -Hp -Hb -Hm -Hn
+[ /2 width=3 by subset_in_eq_repl_back/
+| /5 width=3 by subset_eq_canc_sn, fsubst_eq_repl, lift_term_eq_repl_dx, grafted_eq_repl/
+]
+qed-.
+
+lemma ibfr_eq_repl (t1) (t2) (u1) (u2) (r):
+      t1 ⇔ u1 → t2 ⇔ u2 → t1 ➡𝐢𝐛𝐟[r] t2 → u1 ➡𝐢𝐛𝐟[r] u2.
+/3 width=3 by ibfr_eq_canc_sn, ibfr_eq_trans/
+qed-.