Hello,
Yes i agree, but that's because again you are including frequency not max frequency. It's no mystery that if you lower the frequency you lower the power dissipation, and because it's no mystery we dont need to look at that. What we need to look at is what happens at the max frequency, and that is of primary concern. So when we say the lower bound it's because we are putting a lower bound on the power dissipation at the max frequency. In other words, at the max frequency we can prove that there will always be at least some power dissipation like x watts where x is always going to be greater than some constant.
Lets see if this helps...
For a certain gate we have calculated three power dissipation levels at the max frequency: 0.9 watts, 1.1 watts, 1.2 watts. We are not sure which one it is because of some of the variables in the equation we used to calculate the power dissipation. We can't say for sure what it is, but we know after we consider all variations that we have one of those three. We might be making an error because of the unknowns, so at least we want to know what the best possible power dissipation is that we could ever see, so we chose the lowest one because we know for sure that it can never go lower than that. So if we hoped to use this in a real life circuit, we might be shooting for 1 watt, so then we might have a chance at seeing this criterion met. However, if we calculated the three as: 1.1 watts, 1.2 watts, 1.3 watts, then we know for sure that we could never meet the criterion of 1 watt because the lower bound is 1.1 watts.
So in a real life situation we might be faced with finding out if there is any hope of ever getting this gate to work at the max frequency when we consider the space and air flow restraints we have available to dissipate the power. If the lower bound says "no", then we know we cant do it. If the lower bound says "yes", then there is a chance it might be doable.
It seems that any question about this would come from the 80 percent factor they threw in there. By stating "lower bound" they are implying that the 80 percent is a minimum factor, such that if that goes above 80 percent the power dissipation goes up. So by implication the word 'approximately' may not be the best choice of words.