If it's wrong then it's not provably correct (for any value of 'proof').
How you define your proof is up to you. It might be a simple test, or an exhaustive suite of tests, or a formal proof. It doesn't matter. If the output of the code is correct by your definition, then it doesn't matter what the underlying code actually is.
How you define your proof is up to you. It might be a simple test, or an exhaustive suite of tests, or a formal proof. It doesn't matter. If the output of the code is correct by your definition, then it doesn't matter what the underlying code actually is.