Learn Arabic (Modern Standard): لم تنم بسبب الأرق، بل سهرت حتى الفجر. - She did not sleep because of insomnia, but rather stayed up late until dawn.

The particle لم makes the following present-tense verb take the jussive case. For the hollow verb نام (to sleep), the normal present tense is تنام. When made jussive, the final letter gets a sukoon (no vowel). To avoid having two unvoweled letters in a row, the weak middle letter is dropped, resulting in تنم.

How is بل used differently here than the standard word for but (لكن)?

بل translates to but rather or instead. It is used here after a negative statement (لم تنم) to completely replace the negated action with a contrasting fact. The word لكن just adds contrasting information, whereas بل actively corrects the first statement.

The lesson is about using حتى with past verbs to show a limit. How does that apply here with the noun الفجر?

While حتى is often followed by a past tense verb to show the limit of an action, here it acts as a preposition followed directly by a noun. It serves the exact same lesson purpose: setting the realized end limit of the past action (سهرت). Because حتى is acting as a preposition, الفجر takes a genitive kasra ending.

Does the verb سهرت simply mean she was awake?