theorem
  f1/f - g1/g = (f1(#)g - g1(#)f)/(f(#)g)
proof
  thus f1/f - g1/g = f1/f + ((-1)(#) g1)/g by Th32
    .= (f1(#)g + (-1)(#) g1(#)f)/(f(#)g) by Th40
    .= (f1(#)g - (g1(#)f))/(f(#)g) by Th12;
end;
