Complex sentence: As for the proof of the lemma, it can be derived directly, but a slick way is to show that it is a special case of Hilbert's basis theorem-in fact is essentially the case of ideals generated by monomials.
Split into simpler sentences: As for the proof of the lemma, it can be derived directly, but a slick way is to show that it is a special case of Hilbert's basis theorem. In fact it is essentially the case of ideals generated by monomials.