reserve x for object, X, F for set;
reserve c, c1, c2, c3 for Complex,
  e, e1, e2, e3 for ExtReal,
  r , r1, r2, r3 for Real,
  w, w1, w2, w3 for Rational,
  i, i1, i2, i3 for Integer,
  n, n1, n2, n3 for Nat;

theorem
  for X being non empty rational-membered set ex w st w in X
proof
  let X be non empty rational-membered set;
  ex x being object st x in X by XBOOLE_0:def 1;
  hence thesis;
end;
