
theorem
  for a, b being set st a <> b holds
    {[a, a], [b, b]} <> {[a, a], [a, b], [b, a], [b, b]}
  proof
    let a, b be set;
    assume
AA: a <> b;
    set x1 = [a, a], x2 = [a, b], x3 = [b, a], x4 = [b, b];
A0: x2 <> x1 & x2 <> x4 by AA,XTUPLE_0:1;
    [a, b] in {[a, a], [a, b], [b, a], [b, b]} by ENUMSET1:def 2;
    hence thesis by A0,TARSKI:def 2;
  end;
