 reserve U for set,
         X, Y for Subset of U;
 reserve U for non empty set,
         A, B, C for non empty IntervalSet of U;

theorem Th43:
  for U being non empty set holds
    Inter ([#]U,[#]U) is non empty IntervalSet of U
  proof
    let U be non empty set;
    Inter ([#]U,[#]U) = {[#]U} by Th8;
    hence thesis;
  end;
