However, the important caveat is that induction operates on sets that has well-ordering as an axiom (like the natural numbers); so when well-ordering proves MI, it's showing an extension of itself, and when CI proves well-ordering, it's being consistent with its own axiom that the sets it operates on are well-ordered, and the proof is trivial.
It doesn't feel like anything's being proven when we're using proof techniques that seem tautological (in proving each other, to be fair), but at the very least I can take solace in the fact that they're self-consistent in that they can't contradict each other.
