Syntax of "What proof have we?"

I'm a German and our English teacher always told us not to use the German syntax in English. So here are a few examples to illustrate :

"What means this word?" -> correct : "What does that word mean?" "Have we homework" -> correct :" "Do we have homework?"

That's how I've been taught at least.

I was reading the English version of 'Game of Thrones' today and one sentence is :

"What proof have we?"

Is this sentence correct? I assume it is, since it is a published book. However, if I apply that rule I learned, this would be the correct sentence:

"What proof do we have?"

Where lies the difference?

Your teacher hasn't led you too far astray, because "what proof do we have?" would also be correct, so they wouldn't have led into saying the wrong thing.

English does though sometimes use subject-verb inversion. It happens much more with auxiliaries than other verbs, and one use is in questions:

We have proof.

Have we proof?

We couldn't do that with other verbs, and so would need the do form:

We considered it.

*Considered we it.

Did we consider it?

But auxiliaries don't require this, even when the same verb is being used in a sense other than its auxiliary sense. Adding what we get "what proof have we?"

It's shorter and hence more emphatic than "what proof do we have?". It's also possible that the author's choice was influenced by the fact that earlier in English's history inversion was more common, so while this remains in modern use that may have led the writers to favour it for the work in question.