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diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "basic_2/notation/relations/lazybtpredstarproper_8.ma".
+include "basic_2/reduction/fpb.ma".
+include "basic_2/computation/fpbs.ma".
+
+(* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
+
+definition fpbg: ∀h. sd h → tri_relation genv lenv term ≝
+                 λh,o,G1,L1,T1,G2,L2,T2.
+                 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+
+interpretation "'qrst' proper parallel computation (closure)"
+   'LazyBTPRedStarProper h o G1 L1 T1 G2 L2 T2 = (fpbg h o G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma fpb_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
+                ⦃G1, L1, T1⦄ >≡[h, o] ⦃G2, L2, T2⦄.
+/2 width=5 by ex2_3_intro/ qed.
+
+lemma fpbg_fpbq_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
+                       ⦃G1, L1, T1⦄ >≡[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, o] ⦃G2, L2, T2⦄ →
+                       ⦃G1, L1, T1⦄ >≡[h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
+/3 width=9 by fpbs_strap1, ex2_3_intro/
+qed-.