--- /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/teqg.ma".
+include "static_2/syntax/teqw.ma".
+
+(* SORT-IRRELEVANT WHD EQUIVALENCE ON TERMS *********************************)
+
+(* Properties with generic equivalence for terms ****************************)
+
+lemma teqg_teqw (S):
+ ∀T1,T2. T1 ≛[S] T2 → T1 ≃ T2.
+#S #T1 #T2 #H elim H -T1 -T2 [||| * [ #p ] * #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT ]
+[ /1 width=1 by teqw_sort/
+| /1 width=1 by teqw_lref/
+| /1 width=1 by teqw_gref/
+| cases p -p /2 width=1 by teqw_abbr_pos, teqw_abbr_neg/
+| /1 width=1 by teqw_abst/
+| /2 width=1 by teqw_appl/
+| /2 width=1 by teqw_cast/
+]
+qed.