reserve A for Tolerance_Space,
  X, Y for Subset of A;
reserve A for Approximation_Space,
  X for Subset of A;
reserve A for finite Tolerance_Space,
  X for Subset of A,
  x for Element of A;
reserve A for finite Approximation_Space,
  X, Y for Subset of A,
  x for Element of A;
reserve A for Tolerance_Space,
  X, Y, Z for Subset of A;

theorem Th60:
  X c=^ Y & Y c=^ Z implies X c=^ Z
proof
  assume X c=^ Y & Y c=^ Z;
  then UAp X c= UAp Y & UAp Y c= UAp Z;
  then UAp X c= UAp Z;
  hence thesis;
end;
