Because the proof is for specific people, and these people fully understand this meaning,

Just like some abbreviations, I remember CCTV forcibly changed "NBA" into "American professional basketball league"

The reason is to take care of the audience in front of the TV, because not everyone knows what NBA is.

Ok, this reason is successful, but if a person writes something about NBA technology in the industry,

You can see the NBA completely, because you don't even know the NBA. Are you still an insider?

The proof problem is either for the marking teacher or as a scientific demonstration for a large group of people who are more professional than the marking teacher.

So a "and" is enough.