+(**************************************************************************)
+(* ___ *)
+(* ||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/notation/functions/element_b_2.ma".
+include "ground/relocation/gr_pushs.ma".
+include "ground/relocation/gr_uni.ma".
+
+(* BASIC ELEMENTS FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+definition basic (d) (h): gr_map ≝ ⫯*[d] 𝐮❨h❩.
+
+interpretation
+ "basic elements (generic relocation maps)"
+ 'ElementB d h = (basic d h).
+
+(* Basic properties *********************************************************)
+
+(*** at_basic_succ_sn *)
+lemma gr_basic_succ_sn (d) (h): ⫯𝐛❨d,h❩ = 𝐛❨↑d,h❩.
+#d #h >gr_pushs_succ //
+qed.
+
+(*** at_basic_zero_succ *)
+lemma gr_basic_zero_succ (h): ↑𝐛❨𝟎,h❩ = 𝐛❨𝟎,↑h❩.
+#h >gr_nexts_succ //
+qed.