+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/gr_map.ma".
-
-(* ITERATED PUSH FOR GENERIC RELOCATION MAPS ********************************)
-
-(*** pushs *)
-definition gr_pushs (f:gr_map) (n:nat) ≝
- (gr_push^n) f.
-
-interpretation
- "iterated push (generic relocation maps)"
- 'UpSpoonStar n f = (gr_pushs f n).
-
-(* Basic constructions ******************************************************)
-
-(*** pushs_O *)
-lemma gr_pushs_zero:
- ∀f. f = ⫯*[𝟎] f.
-// qed.
-
-(*** push_swap *)
-lemma gr_pushs_push (n):
- ∀f. ⫯⫯*[n] f = ⫯*[n] ⫯f.
-#n #f @(niter_appl … gr_push)
-qed.
-
-(*** pushs_S *)
-lemma gr_pushs_succ (n):
- ∀f. ⫯⫯*[n] f = ⫯*[↑n] f.
-#f #n @(niter_succ … gr_push)
-qed.
-
-(*** pushs_xn *)
-lemma gr_pushs_swap (n):
- ∀f. ⫯*[n] ⫯f = ⫯*[↑n] f.
-// qed.