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 Th18:
  for f being homogeneous Relation st dom f = {{}} holds arity f = 0
proof
  let f be homogeneous Relation;
  assume dom f = {{}};
  then {} in dom f by TARSKI:def 1;
  hence thesis by CARD_1:27,MARGREL1:def 25;
end;
