matita/matita/contribs/lambdadelta/delayed_updating/relocation/tr_minus.ma

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  14
  15 include "ground/arith/pnat_minus.ma".
  16 include "ground/arith/nat_minus.ma".
  17 include "ground/relocation/tr_map.ma".
  18
  19 (* RIGHT SUBTRACTION FOR TOTAL RELOCATION MAPS ******************************)
  20
  21 corec definition tr_minus: nat → tr_map → tr_map.
  22 * [ #f @f ] #q * #p #f
  23 @((p-q)⨮(tr_minus (ninj (↑q)-ninj p) f))
  24 defined.
  25
  26 interpretation
  27   "right minus (total relocation maps)"
  28   'minus f n = (tr_minus n f).
  29
  30 (* Basic constructions ******************************************************)
  31
  32 lemma tr_minus_zero_dx (f):
  33       f = f - 𝟎 .
  34 * #f #p <(stream_unfold … ((f⨮p)-𝟎)) //
  35 qed.
  36
  37 lemma tr_minus_cons_inj (f) (p) (q):
  38       (p-q)⨮(f-(ninj (↑q)-ninj p)) = (p⨮f)-(ninj q).
  39 #f #p #q <(stream_unfold … ((p⨮f)-(ninj q))) //
  40 qed.