Sometimes, discovering these proofs makes the math easier. If we know X is the case for all Ys, and X is easier to compute, you can use X where you would use Y

Sometimes, discovering these proofs makes the math easier. If we know X is the case for all Ys, and X is easier to compute, you can use X where you would use Y before. Of if you know X is true for all Ys, you can skip the part where you have to verify that your Y has X property. Because we now know it must have it. And it's math all the way down in computers. So anything that makes math easier or quicker has the potential to affect anything a computer can process.