--- /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/syntax/ext2.ma".
+
+(* EXTENSION TO BINDERS OF A RELATION FOR TERMS *****************************)
+
+(* Main properties **********************************************************)
+
+theorem ext2_trans: ∀R. Transitive … R → Transitive … (ext2 R).
+#R #HR #I1 #I #H elim H -I1 -I
+[ #I1 #J #H >(ext2_inv_unit_sn … H) -J /2 width=1 by ext2_unit/
+| #I1 #V1 #V #HV1 #J #H elim (ext2_inv_pair_sn … H) -H
+ #V2 #HV2 #H destruct /3 width=3 by ext2_pair/
+]
+qed-.