
theorem Lemma11:
  for a, b being set st a <> b holds
    {[a, a], [b, b]} misses {[a, b], [b, a]}
  proof
    let a, b be set;
    assume a <> b; then
A0: [a,b] <> [a,a] & [a,b] <> [b,b] & [a,b] <> [b,a] & [a,a] <> [b,a]
      & [b,b] <> [b,a] by XTUPLE_0:1;
    set A = {[a, a], [b, b]}, B = {[a, b], [b, a]};
    assume A meets B; then
    consider x being object such that
A1: x in A & x in B by XBOOLE_0:3;
    x = [a,a] or x = [b,b] by A1,TARSKI:def 2;
    hence thesis by A0,A1,TARSKI:def 2;
  end;
