+(**************************************************************************)
+(* ___ *)
+(* ||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/stream_hdtl.ma".
+include "ground/lib/stream_eq.ma".
+
+(* HEAD AND TAIL FOR STREAMS ************************************************)
+
+(* Constructions with stream_eq *********************************************)
+
+lemma stream_hd_eq_repl (A):
+ stream_eq_repl A (λt1,t2. ⇃t1 = ⇃t2).
+#A * #a1 #t1 * #a2 #t2 #H
+elim (stream_eq_inv_cons_bi … H) -H
+/2 width=7 by/
+qed.
+
+lemma stream_tl_eq_repl (A):
+ stream_eq_repl A (λt1,t2. ⇂t1 ≗ ⇂t2).
+#A * #a1 #t1 * #a2 #t2 #H
+elim (stream_eq_inv_cons_bi … H) -H
+/2 width=7 by/
+qed.