But you can easily answer of course, which is because induction can't not work.
For it to not work there has to be a step N where the N-1 step satisfies the claim proven and the Nth step violates the claim. By hypothesis this is exactly what you have proven to never happen in the inductive step of the proof.
Probably GP will then answer with something like "how do you know that N-1 works" or something equally obnoxious. (It's not obnoxious because it's an invalid question, it's obnoxious because GP is just being a pain at that point, and coming up with objections to be annoying but without actually caring about the answer. It's like if you answer every statement anyone ever makes with "I would like to respond, but I can't be sure you aren't an evil demon sent to trick me, or a foreigner who speaks a language that sounds exactly like english but with a completely different meaning.")
For it to not work there has to be a step N where the N-1 step satisfies the claim proven and the Nth step violates the claim. By hypothesis this is exactly what you have proven to never happen in the inductive step of the proof.
Probably GP will then answer with something like "how do you know that N-1 works" or something equally obnoxious. (It's not obnoxious because it's an invalid question, it's obnoxious because GP is just being a pain at that point, and coming up with objections to be annoying but without actually caring about the answer. It's like if you answer every statement anyone ever makes with "I would like to respond, but I can't be sure you aren't an evil demon sent to trick me, or a foreigner who speaks a language that sounds exactly like english but with a completely different meaning.")