User blog comment:Wythagoras/Proof that TREE(n+1) divided by TREE(n) is strictly increasing/@comment-99.185.0.100-20150917002400/@comment-5529393-20150917073844

Ah, that's true. But then the difficulty is showing that BB(n+1) > BB(n)+1; the point is that the threshold of provability is way less than the growth rate that we expect.