 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 Th55:
  for X being Tolerance_Space, A being RoughSet of X holds
    ex B, C being Subset of X st A = [B,C]
  proof
    let X be Tolerance_Space,
        A be RoughSet of X;
    consider A1, A2 being object such that
A1: A1 in bool the carrier of X & A2 in bool the carrier of X & A = [A1,A2]
      by ZFMISC_1:def 2;
    reconsider A1, A2 as Subset of X by A1;
    take A1, A2;
    thus thesis by A1;
  end;
