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

theorem Th31:
  for a,b being Real holds IRRAT (a,b) c= [.a,+infty .[
proof
  let a,b be Real;
    let x be object;
    assume
A1: x in IRRAT (a,b);
    then reconsider x as Real;
    a < x by A1,BORSUK_5:30;
    hence thesis by XXREAL_1:236;
end;
