The bank won't give proof, so the loan can't come down.

The key to this matter is that the bank does not refuse to lend, but only gives 200 thousand loans, so the certificate that you can't borrow from the bank will not be given to you, because it is not in line with the actual situation. You can change the way: you can ask the bank to issue a certificate that the maximum loan can only be 200 thousand, and then take this certificate to the housing authority for negotiation, which should be useful.