Anki is a digital flash card app for phones, so I guess they convert whatever they’re learning to the Anki format.

Look up Avogadro

OK, you got it then, I believe. P3 is specifically built so that P3(xn)=yn for n from 1 to 4. The proof lies in its construction. I guess the sentence can be understood as “we know it works because we built it like that, however you may verify it yourself”

Replace the words “Convince yourself” with “You can verify” and it might make more sense.