In particular, the student’s version of TeXmacs could get the lecture notes in advance from their professor (in TeXmacs format) and then use them to autocorrect and autocomplete the student’s notes during the lecture as they make them in real-time.
The student could even take rough notes with a pen and have the app automatically convert them to TeXmacs format in a way that preserves some of the student’s formatting and is 100% accurate with respect to the professor’s lecture notes.