
theorem FR1:
  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;
