[Reisen]

This is a correct intuition yes. A program written in Cairo taking your balance (private) and a minimum collateral (public) and outputs a boolean for pass/fail, where the lender can only see "pass/fail" but trust the program was executed correctly is right.

However the technology isn't particularly useful in this scenario. It's enough for your bank to just reply to a request with "yes" without running the program because in theory you are forced to trust the bank no matter what as you have no guarantee the bank didn't just lie about your balance in the input to the Cairo program, so in this scenario the proof doesn't bring much. This technology is a lot more useful when the data being verified is combined with something that guarantees that the data input wasn't forged somehow, which is why this is more useful in blockchain environments where all transactions and balances are signed, so someone can't just invent a balance out of thin air.