--- /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/s_transition/fqu_length.ma".
+include "basic_2/s_transition/fquq.ma".
+
+(* OPTIONAL SUPCLOSURE ******************************************************)
+
+(* Forward lemmas with length for local environments ************************)
+
+lemma fquq_fwd_length_lref1: ∀G1,G2,L1,L2,T2,i. ⦃G1, L1, #i⦄ ⊐⸮ ⦃G2, L2, T2⦄ → |L2| ≤ |L1|.
+#G1 #G2 #L1 #L2 #T2 #i #H elim H -H [2: * ]
+/3 width=5 by fqu_fwd_length_lref1, lt_to_le/
+qed-.