>>10829264If you have a function then any finite number of iterations of that function is still just a function with the same domain. Prove this by induction.
All you have to prove is that TREE(n) is a function in the first place, meaning it can only map a given n to one specific natural number TREE(n).
To do this, you need to use the definition of TREE(n). I think it's some kind of graph Ramsey theorem. Go read whatever paper it is from.
