matita/matita/contribs/lambdadelta/ground/arith/nat_rplus.ma

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  14
  15 include "ground/arith/nat_iter.ma".
  16
  17 (* RIGHT ADDITION FOR NON-NEGATIVE INTEGERS *********************************)
  18
  19 definition nrplus: pnat → nat → pnat ≝
  20            λp,n. psucc^n p.
  21
  22 interpretation
  23   "right plus (non-negative integers)"
  24   'plus p n = (nrplus p n).
  25
  26 (* Basic constructions ******************************************************)
  27
  28 lemma nrplus_zero_dx (p): p = p + 𝟎.
  29 // qed.
  30
  31 lemma nrplus_unit_dx (p): ↑p = p + 𝟏.
  32 // qed.
  33
  34 lemma nrplus_succ_sn (p) (n): ↑(p+n) = ↑p + n.
  35 #p #n @(niter_appl … psucc)
  36 qed.