If you could double spend I don't think we'd be discussing it any further

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Bob mints token A, copies it and redeems it with the mint. Bob uses the copy of token A to buy apples from Alice. Alice sends apples over as she can see she received a valid token (minted from the same mint).

Alice goes to redeem the token copy and gets a "token already redeemed" from the mint.

Maybe it's not exactly double-spending, but it permits some sort of fraud?

Otherwise, if you assume the tokens are redeemed (for BTC LN) automatically with the mint on every transaction, how is it better/more private than BTC LN alone?

Genuine question, I'm just a beginner trying to understand Cashu on top of LN