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 be with_the_same_arity FinSequence st len F = 0 holds arity F = 0
proof
  let F be with_the_same_arity FinSequence;
  assume len F = 0;
  then F = {};
  then for f being homogeneous Function holds not f in rng F;
  hence thesis by Def4;
end;
