reserve T for TopSpace,
  A, B for Subset of T;

theorem
  for a,b being Real st a >= b holds IRRAT (a,b) = {}
proof
  let a, b be Real;
  assume
A1: a >= b;
  IRRAT (a,b) = IRRAT /\ ]. a, b .[ by BORSUK_5:def 3
    .= IRRAT /\ {} by A1,XXREAL_1:28;
  hence thesis;
end;
