> And what if the cashu you gave me you received from yet someone first?

A Cashu token is a bearer asset, so whoever has a copy of it can spend it (unless it is locked to you). So if someone gives you a token, you should "receive" it to your wallet asap.

When you do this, your wallet will send it to the mint, and the mint will invalidate it and issue you a brand new tokan.

That way, if other people have a copy of the old token, it is already "spent" on creating you a new one.