--- /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/term_simple.ma".
+include "static_2/syntax/tweq.ma".
+
+(* SORT-IRRELEVANT WHD EQUIVALENCE ON TERMS *********************************)
+
+(* Properties with simple terms *********************************************)
+
+lemma tweq_simple_trans:
+ ∀T1,T2. T1 ≅ T2 → 𝐒⦃T1⦄ → 𝐒⦃T2⦄.
+#T1 #T2 * -T1 -T2
+[4,5: #p #V1 #V2 #T1 #T2 [ #_ ] #H
+ elim (simple_inv_bind … H)
+|* : /1 width=1 by simple_atom, simple_flat/
+]
+qed-.