1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "ground/notation/functions/upspoonstar_2.ma".
16 include "ground/arith/nat_succ_iter.ma".
17 include "ground/relocation/tr_pn.ma".
19 (* ITERATED PUSH FOR TOTAL RELOCATION MAPS **********************************)
21 definition tr_pushs (f:tr_map) (n:nat) ≝
25 "iterated push (total relocation maps)"
26 'UpSpoonStar n f = (tr_pushs f n).
28 (* Basic constructions ******************************************************)
34 lemma tr_pushs_push (n):
35 ∀f. ⫯⫯*[n] f = ⫯*[n] ⫯f.
36 #n #f @(niter_appl … tr_push)
39 lemma tr_pushs_succ (n):
40 ∀f. ⫯⫯*[n] f = ⫯*[↑n] f.
41 #f #n @(niter_succ … tr_push)
44 lemma tr_pushs_swap (n):
45 ∀f. ⫯*[n] ⫯f = ⫯*[↑n] f.