And it's relatively easy to prove intuitively. If you pick a random point in time, the time from that point to the point of finding the next block will be 10 mi

And it's relatively easy to prove intuitively. If you pick a random point in time, the time from that point to the point of finding the next block will be 10 minutes. That is globally true. The point will also be randomly distributed in an interval, so on average there is as much time between the random point and the next block as between the random point and the previous block. Thus at a random point in time the average interval is 10 minutes + 10 minutes = 20 minutes.