
theorem FR2:
  for a,b be Real holds
    frac (a*b) = frac (([\a/]*frac b) + ([\b/]*frac a) + (frac a)*(frac b))
  proof
    let a,b be Real;
    a = [\a/] + frac a & b = [\b/] + frac b by INT_1:42; then
    frac (a*b) =
       frac ([\a/]*[\b/] + (([\a/]*frac b) + ([\b/]*frac a) +
         (frac a)*(frac b)))
    .= frac (([\a/]*frac b) + ([\b/]*frac a) + (frac a)*(frac b)) by INT_1:66;
    hence thesis;
  end;
