reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T,
  x for set;

theorem
  for A being Subset of R^1 st A = IRRAT holds Int A = {}
proof
  let A be Subset of R^1;
  assume A = IRRAT;
  then Cl A` = [#]R^1 by Lm2,BORSUK_5:15,TOPMETR:17;
  then (Cl A`)` = {}R^1 by XBOOLE_1:37;
  hence thesis by Th3;
end;
