It isn't induction exactly. The proof works without it, but to get the right initial index I picked a set whose order I could easily count as the starting point.
At least I think that's how it went.
Discussion
I only gave a short look after Wikipedia skim of what the sieves were, so maybe missed something. Will come back to it when my fiat overlords aren't suppressing my curiosity of things outside spreadsheets 🥲
Looked again and still seems like induction to me, but I'll take your word for it since there are too many symbols I'm only vaguely guessing at from context. Number theory hurts my brain
You are probably right. Like I said. I am bad at proofs. I do like some number theory though. I'll have to dig into those fantasy numbers at some point. They may have some tricks I could use.