That´s incredible and a good news ! When I was a student of Computer Since (25 years ago) teachers forced us to use symbols instead of words. Things are going better ;)

One question ... you use "and" insteed of "$\land$" ??

@MikhailBorovoi that was I would to say in the previous comment.

@NoahSchweber It sounds very reasonable, I'm glad to read you. However, I feel that it is not exactly the same definition, it seems not to be an indexed family. Furthermore, it seems that each definition is going to be very extensive including motivation. I usually present some definitions to "build" another bigger showing the motivation of them togother. I don't know it can be weak syllogism.