--- /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/s_transition/fqu_weight.ma".
+include "static_2/s_transition/fquq.ma".
+
+(* OPTIONAL SUPCLOSURE ******************************************************)
+
+(* Forward lemmas with weight for closures **********************************)
+
+lemma fquq_fwd_fw: ∀b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
+ ♯{G2, L2, T2} ≤ ♯{G1, L1, T1}.
+#b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -H [2: * ]
+/3 width=2 by fqu_fwd_fw, lt_to_le/
+qed-.