--- /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/syntax/tdeq.ma".
+include "static_2/syntax/theq.ma".
+
+(* HEAD EQUIVALENCE FOR TERMS ***********************************************)
+
+(* Properties with degree-based equivalence for terms ***********************)
+
+lemma tdeq_theq: ∀h,o,T1,T2. T1 ≛[h, o] T2 → T1 ⩳[h, o] T2.
+#h #o #T1 #T2 * -T1 -T2 /2 width=3 by theq_sort, theq_pair/
+qed.