reserve A for Tolerance_Space,
  X, Y for Subset of A;

theorem Th13:
  X c= UAp X
proof
  let x be object;
  assume
A1: x in X;
  then reconsider x9 = x as Element of A;
  x9 in Class (the InternalRel of A, x9) by EQREL_1:20;
  then Class (the InternalRel of A, x9) meets X by A1,XBOOLE_0:3;
  hence thesis;
end;
