--- /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 "basic_2/notation/relations/suptermopt_6.ma".
+include "basic_2/s_transition/fqu.ma".
+
+(* OPTIONAL SUPCLOSURE ******************************************************)
+
+(* Basic_2A1: was: fquqa *)
+(* Basic_2A1: includes: fquq_inv_gen *)
+definition fquq: tri_relation genv lenv term ≝ tri_RC … fqu.
+
+interpretation
+ "optional structural successor (closure)"
+ 'SupTermOpt G1 L1 T1 G2 L2 T2 = (fquq G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+(* Basic_2A1: includes: fquqa_refl *)
+lemma fquq_refl: tri_reflexive … fquq.
+// qed.
+
+lemma fqu_fquq: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ⊐⸮ ⦃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
+*)