theorem Th1:
  for a, b being Real holds max(a,b) >= min(a,b)
proof
  let a, b be Real;
  per cases by XXREAL_0:15;
  suppose
    min(a,b)=a;
   hence thesis by XXREAL_0:25;
  end;
  suppose
    min(a,b)=b;
    hence thesis by XXREAL_0:25;
  end;
end;
