+(**************************************************************************)
+(* ___ *)
+(* ||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/upspoonstar_2.ma".
+include "ground/arith/nat_succ_iter.ma".
+include "ground/relocation/tr_pn.ma".
+
+(* ITERATED PUSH FOR TOTAL RELOCATION MAPS **********************************)
+
+definition tr_pushs (f:tr_map) (n:nat) ≝
+ (tr_push^n) f.
+
+interpretation
+ "iterated push (total relocation maps)"
+ 'UpSpoonStar n f = (tr_pushs f n).
+
+(* Basic constructions ******************************************************)
+
+lemma tr_pushs_zero:
+ ∀f. f = ⫯*[𝟎] f.
+// qed.
+
+lemma tr_pushs_push (n):
+ ∀f. ⫯⫯*[n] f = ⫯*[n] ⫯f.
+#n #f @(niter_appl … tr_push)
+qed.
+
+lemma tr_pushs_succ (n):
+ ∀f. ⫯⫯*[n] f = ⫯*[↑n] f.
+#f #n @(niter_succ … tr_push)
+qed.
+
+lemma tr_pushs_swap (n):
+ ∀f. ⫯*[n] ⫯f = ⫯*[↑n] f.
+// qed.