When proving you should to prove that they are similar and not that they are dissimilar.

Let me meditate on that.

Please use an LLM and prove it yourself. Then use an LLM and prove the opposite. That's how much weight your "proofs" have.

In fact, buy a premium subscription to all the LLMs out there (yes, even LLAMA) and have them write the proof using the scientific method, and submit the papers to me via a carrier pigeon.