so i spent most of the day LaTeX'ing, which went well enough.
the best thing about writing up ready results in LaTeX is that one feels smart, that maybe all those days of banging one's head against these damned technical lemmas  were worth it after all.
.. on the other hand, there's something else I should write up, but i can't convince myself to do so:
whenever i think about the proof, I don't feel smart. instead, it just seems .. trivial.
 technically, the plural of lemma is "lemmata."