theorem
  p < q iff numerator(p)*denominator(q) < numerator(q)*denominator(p)
proof
  p<q iff numerator(p)/denominator(p)<q by Th12;
  then
  p<q iff numerator(p)/denominator(p)<numerator(q)/denominator(q) by Th12;
  hence thesis by XREAL_1:102,106;
end;
