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
  n <> 0 implies n-tuples_on {} = {}
proof
  assume that
A1: n <> 0 and
A2: n-tuples_on {} <> {};
  consider x being object such that
A3: x in n-tuples_on {} by A2;
  ex s being Element of {}* st s = x & len s = n by A3;
  hence contradiction by A1;
end;
