 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 Th26:
  for A being non empty IntervalSet of U holds
    A is non empty ordered Subset-Family of U
  proof
    let A be non empty IntervalSet of U;
    A = Inter (A``1,A``2) & A``1 c= A``2 by Th15,Th16;
    hence thesis by Th25;
  end;
