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

theorem Th20:
  LAp [#]A = [#]A
proof
  thus LAp [#]A c= [#]A;
  let x be object;
A1: Class (the InternalRel of A, x) c= [#]A;
  assume x in [#]A;
  hence thesis by A1;
end;
