
theorem
  for x1, x2, x3, x4, x5, x6 being set holds { x1, x2, x3, x4, x5, x6 }
  = { x1, x3, x6 } \/ { x2, x4, x5 }
proof
  let x1, x2, x3, x4, x5, x6 be set;
  thus { x1, x2, x3, x4, x5, x6 } c= { x1, x3, x6 } \/ { x2, x4, x5 }
  proof
    let x be object;
    assume x in { x1, x2, x3, x4, x5, x6 };
    then x = x1 or x = x2 or x = x3 or x = x4 or x = x5 or x = x6 by
ENUMSET1:def 4;
    then x in { x1, x3, x6 } or x in { x2, x4, x5 } by ENUMSET1:def 1;
    hence thesis by XBOOLE_0:def 3;
  end;
  let x be object;
  assume x in { x1, x3, x6 } \/ { x2, x4, x5 };
  then x in { x1, x3, x6 } or x in { x2, x4, x5 } by XBOOLE_0:def 3;
  then x = x1 or x = x3 or x = x6 or x = x2 or x = x4 or x = x5 by
ENUMSET1:def 1;
  hence thesis by ENUMSET1:def 4;
end;
