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/uparrowstar_2.ma".
16 include "ground/arith/nat_succ_iter.ma".
17 include "ground/relocation/pr_map.ma".
19 (* ITERATED NEXT FOR PARTIAL RELOCATION MAPS ********************************)
22 definition pr_nexts (f:pr_map) (n:nat) ≝
26 "iterated next (partial relocation maps)"
27 'UpArrowStar n f = (pr_nexts f n).
29 (* Basic constructions ******************************************************)
37 lemma pr_nexts_next (n):
38 ∀f. ↑↑*[n] f = ↑*[n] ↑f.
39 #f #n @(niter_appl … pr_next)
43 lemma pr_nexts_succ (n):
44 ∀f. ↑↑*[n] f = ↑*[↑n] f.
45 #f #n @(niter_succ … pr_next)
49 lemma pr_nexts_swap (n):
50 ∀f. ↑*[n] ↑f = ↑*[↑n] f.