User blog comment:B1mb0w/General Proof of Strong D Function Growth Rate/@comment-5529393-20150809072224/@comment-5529393-20150809074957

Yes, there is an error. You have to remember exactly what you proved. The statement you proved was exactly: (here I am combining your fifth and sixth proofs into one since they go together)

If $$D(l-1,0,n) > f_{\phi-1}^n(f_\phi(n))$$ and $$D(l-1,m,n) > f_{\phi-1}^{m+n}(f_\phi(m))$$

then $$D(l,0,n) > f_{\phi}^n(f_{\phi+1}(n))$$ and $$D(l,m,n) > f_{\phi}^{m+n}(f_{\phi+1}(m))$$

No more, no less. So to apply this statement, you must prove that $$D(l-1,0,n) > f_{\phi-1}^n(f_\phi(n))$$ and $$D(l-1,m,n) > f_{\phi-1}^{m+n}(f_\phi(m))$$ for some value of. Proving $$D(m,m,0) > f_{\omega 2}(m)$$ gets you exactly nothing, since there is no theorem with that particular assumption.