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Auxiliary Notions

All further definitions work for both constructions of the naturals.

• Subsets of the natural numbers:

  N>0	:=	{x in N: x > 0};
  Nn	:=	{x in N: x < n}.

  e.g. N₃ = {0, 1, 2}.
• Predecessor function:

  x- := such y: x = y'.

  e.g. 3^- = 2; 0^- = ?.