matita/matita/contribs/lambdadelta/ground/relocation/tr_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/tr_pn.ma".
  18
  19 (* ITERATED PUSH FOR TOTAL RELOCATION MAPS **********************************)
  20
  21 definition tr_pushs (f:tr_map) (n:nat) ≝
  22            (tr_push^n) f.
  23
  24 interpretation
  25   "iterated push (total relocation maps)"
  26   'UpSpoonStar n f = (tr_pushs f n).
  27
  28 (* Basic constructions ******************************************************)
  29
  30 lemma tr_pushs_zero:
  31       ∀f. f = ⫯*[𝟎] f.
  32 // qed.
  33
  34 lemma tr_pushs_push (n):
  35       ∀f. ⫯⫯*[n] f = ⫯*[n] ⫯f.
  36 #n #f @(niter_appl … tr_push)
  37 qed.
  38
  39 lemma tr_pushs_succ (n):
  40       ∀f. ⫯⫯*[n] f = ⫯*[↑n] f.
  41 #f #n @(niter_succ … tr_push)
  42 qed.
  43
  44 lemma tr_pushs_swap (n):
  45       ∀f. ⫯*[n] ⫯f = ⫯*[↑n] f.
  46 // qed.