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

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  14
  15 include "ground/notation/functions/upspoonstar_2.ma".
  16 include "ground/arith/nat_succ_iter.ma".
  17 include "ground/relocation/pr_map.ma".
  18
  19 (* ITERATED PUSH FOR PARTIAL RELOCATION MAPS ********************************)
  20
  21 (*** pushs *)
  22 definition pr_pushs (f:pr_map) (n:nat) ≝
  23            (pr_push^n) f.
  24
  25 interpretation
  26   "iterated push (partial relocation maps)"
  27   'UpSpoonStar n f = (pr_pushs f n).
  28
  29 (* Basic constructions ******************************************************)
  30
  31 (*** pushs_O *)
  32 lemma pr_pushs_zero:
  33       ∀f. f = ⫯*[𝟎] f.
  34 // qed.
  35
  36 (*** push_swap *)
  37 lemma pr_pushs_push (n):
  38       ∀f. ⫯⫯*[n] f = ⫯*[n] ⫯f.
  39 #n #f @(niter_appl … pr_push)
  40 qed.
  41
  42 (*** pushs_S *)
  43 lemma pr_pushs_succ (n):
  44       ∀f. ⫯⫯*[n] f = ⫯*[↑n] f.
  45 #f #n @(niter_succ … pr_push)
  46 qed.
  47
  48 (*** pushs_xn *)
  49 lemma pr_pushs_swap (n):
  50       ∀f. ⫯*[n] ⫯f = ⫯*[↑n] f.
  51 // qed.