-(**************************************************************************)
-(* ___ *)
-(* ||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/prototerm.ma".
-
-(* EQUIVALENCE FOR PROTOTERM ************************************************)
-
-(* Constructions with prototerm_root ****************************************)
-
-lemma prototerm_root_incl_repl:
- ∀t1,t2. t1 ⊆ t2 → ▵t1 ⊆ ▵t2.
-#t1 #t2 #Ht #p * #q #Hq
-/3 width=2 by ex_intro/
-qed.
-
-lemma prototerm_root_eq_repl:
- ∀t1,t2. t1 ⇔ t2 → ▵t1 ⇔ ▵t2.
-#t1 #t2 * #H1 #H2
-/3 width=3 by conj, prototerm_root_incl_repl/
-qed.