I am currently reading the appendices of Higher Topos Theory, and I was puzzled by Lurie's proof of lemma A.2.6.7 (I can not make sense of the end of the proof.)

He uses this result to prove Jeff Smith's theorem, but the proof on the n lab (https://ncatlab.org/nlab/revision/combinatorial+model+category/59) does not seem to use such a technical preliminary result.

So I am wondering why does Lurie's proof is this much more complicated? And, if the added complexity is somehow necessary for the proof to work, could someone point out the "mistake" in the n lab and give reference?

the proof on n Labyou mean the proof given in the article combinatorial model category (current revision)? Perhaps adding a link might be useful for the potential answerers. $\endgroup$ – Martin Sleziak Dec 31 '18 at 9:02