reserve i, j, k, c, m, n for Nat,
  a, x, y, z, X, Y for set,
  D, E for non empty set,
  R for Relation,
  f, g for Function,
  p, q for FinSequence;

theorem
  for f being homogeneous to-naturals NAT*-defined Function holds
  arity <*f*> = arity f
proof
  let f be homogeneous to-naturals NAT*-defined Function;
  rng <*f*> = {f} by FINSEQ_1:38;
  then f in rng <*f*> by TARSKI:def 1;
  hence thesis by Def4;
end;
