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 Th5:
  0-tuples_on X = {{}}
proof
  set S = {s where s is Element of X*: len s = 0};
  now
    let x be object;
    hereby
      assume x in S;
      then consider s being Element of X* such that
A1:   x = s and
A2:   len s = 0;
      s = {} by A2;
      hence x in {{}} by A1,TARSKI:def 1;
    end;
    assume x in {{}};
    then
A3: x = {} by TARSKI:def 1;
    <*>(X*) is Element of X* by FINSEQ_1:49;
    hence x in S by A3,CARD_1:27;
  end;
  hence thesis;
end;
