+(**************************************************************************)
+(* ___ *)
+(* ||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 "ground/lib/subset_equivalence.ma".
+include "delayed_updating/syntax/preterm.ma".
+
+(* EQUIVALENCE FOR PRETERM **************************************************)
+
+(* Constructions with preterm_root ******************************************)
+
+lemma preterm_root_incl_repl:
+ βt1,t2. t1 β t2 β β΅t1 β β΅t2.
+#t1 #t2 #Ht #p * #q #Hq
+/3 width=2 by ex_intro/
+qed.
+
+lemma preterm_root_eq_repl:
+ βt1,t2. t1 β t2 β β΅t1 β β΅t2.
+#t1 #t2 * #H1 #H2
+/3 width=3 by conj, preterm_root_incl_repl/
+qed.