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

theorem Th10:
  for x being set st x in UAp X holds Class (the InternalRel of A, x) meets X
proof
  let x be set;
  assume x in UAp X;
  then ex x1 being Element of A st x = x1 & Class (the InternalRel of A, x1)
  meets X;
  hence thesis;
end;
