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diff --git a/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq.ma b/matita/matita/contribs/lambdadelta/static_2/s_transition/fquq.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 "static_2/notation/relations/suptermopt_6.ma".
+include "static_2/notation/relations/suptermopt_7.ma".
+include "static_2/s_transition/fqu.ma".
+
+(* OPTIONAL SUPCLOSURE ******************************************************)
+
+(* Basic_2A1: was: fquqa *)
+(* Basic_2A1: includes: fquq_inv_gen *)
+definition fquq: bool → tri_relation genv lenv term ≝
+                 λb. tri_RC … (fqu b).
+
+interpretation
+   "extended optional structural successor (closure)"
+   'SupTermOpt b G1 L1 T1 G2 L2 T2 = (fquq b G1 L1 T1 G2 L2 T2).
+
+interpretation
+   "optional structural successor (closure)"
+   'SupTermOpt G1 L1 T1 G2 L2 T2 = (fquq true G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+(* Basic_2A1: includes: fquqa_refl *)
+lemma fquq_refl: ∀b. tri_reflexive … (fquq b).
+// qed.
+
+lemma fqu_fquq: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄.
+/2 width=1 by or_introl/ qed.
+
+(* Basic_2A1: removed theorems 8:
+              fquq_lref_O fquq_pair_sn fquq_bind_dx fquq_flat_dx fquq_drop
+              fquqa_drop fquq_fquqa fquqa_inv_fquq
+*)