
theorem Lemma6:
  for x1, x2, x3, x4 being set holds
    {x1} \/ {x2} \/ {x3, x4} = {x3, x1, x2, x4}
  proof
    let x1, x2, x3, x4 be set;
    {x1} \/ {x2} \/ {x3, x4} = {x1, x2} \/ {x3, x4} by ENUMSET1:1
      .= {x1, x2, x3, x4} by ENUMSET1:5
      .= {x3, x2, x1, x4} by ENUMSET1:71
      .= {x3} \/ {x2, x1, x4} by ENUMSET1:4
      .= {x3} \/ {x1, x2, x4} by ENUMSET1:58
      .= {x3, x1, x2, x4} by ENUMSET1:4;
    hence thesis;
  end;
