 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 Th40:
  A _\_ B = Inter (A``1 \ B``2, A``2 \ B``1)
  proof
    reconsider AA = A, BB = B as non empty ordered Subset-Family of U
      by Th26;
    AA = Inter (A``1,A``2) & BB = Inter (B``1,B``2) by Th15; then
    min AA = A``1 & min BB = B``1 & max AA = A``2 & max BB = B``2 by Th27;
    hence thesis by Th38;
  end;
