+(**************************************************************************)
+(* ___ *)
+(* ||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 "delayed_updating/syntax/path_dhd.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_depth.ma".
+
+(* HEAD BY DEPTH FOR PATH ***************************************************)
+
+(* Constructions with structure *********************************************)
+
+lemma path_dhd_structure_L_sn (p) (q):
+ let r ≝ 𝗟◗p in
+ ⊗r = ↳⧣[♭⊗r]((⊗r)●q).
+#p elim p -p //
+* [ #n ] #p #IH #q //
+ [ <structure_L_sn //
+ | <structure_A_sn <list_append_lcons_sn
+ <path_head_A_sn //
+ | <structure_S_sn //
+ ]
+]
+*)
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