matita/matita/contribs/lambdadelta/ground/relocation/gr_nexts.ma

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   3 (*      ||M||                                                             *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "ground/notation/functions/uparrowstar_2.ma".
  16 include "ground/arith/nat_succ_iter.ma".
  17 include "ground/relocation/gr_map.ma".
  18
  19 (* ITERATED NEXT FOR GENERIC RELOCATION MAPS ********************************)
  20
  21 (*** nexts *)
  22 definition gr_nexts (f:gr_map) (n:nat) ≝
  23            (gr_next^n) f.
  24
  25 interpretation
  26   "iterated next (generic relocation maps)"
  27   'UpArrowStar n f = (gr_nexts f n).
  28
  29 (* Basic constructions ******************************************************)
  30
  31 (*** nexts_O *)
  32 lemma gr_nexts_zero:
  33       ∀f. f = ↑*[𝟎] f.
  34 // qed.
  35
  36 (*** nexts_swap *)
  37 lemma gr_nexts_next (n):
  38       ∀f. ↑↑*[n] f = ↑*[n] ↑f.
  39 #f #n @(niter_appl … gr_next)
  40 qed.
  41
  42 (*** nexts_S *)
  43 lemma gr_nexts_succ (n):
  44       ∀f. ↑↑*[n] f = ↑*[↑n] f.
  45 #f #n @(niter_succ … gr_next)
  46 qed.
  47
  48 (*** nexts_xn *)
  49 lemma gr_nexts_swap (n):
  50       ∀f. ↑*[n] ↑f = ↑*[↑n] f.
  51 // qed.