Learn English – Usage of “no longer are” vs “are no longer”

Indeed, I see nothing wrong either with the sentence as written, though I would suspect it more common for the sentence to take the opposite perspective:

I am proud to be your daughter/son

In either case you would be proud of his personality or his achievements in life. Of course such achievements might be simply having other great children, however it would be far nearer to be proud of him for something else/more.

Saying that some number of slots are filled but that number could be any number between 0 and ALL means, simply, "Any number of slots could be filled. Or not."

The only real restriction you are placing on the description is that any slots that are filled are filled "front to back" or "first to last".

As far as "plain English", one phrase that will help is "so many". This simply means "an unknown number":

1. The first so many slots are filled. (PROBLEM: Heavily implies at least one.)

2. Slots should be filled first to last. (PROBLEM: Only notes the criteria.)

3. If slots are filled, they are the first so many slots. (Satisfies your criteria by specifically noting that none could be filled.)

4. Any slots filled are filled front to back. (Satisfies your criteria as this implies some number could be filled and it describes the condition.)

I think (4) is the easiest to understand and the most English-y but (3) is technically most similar to your given criteria.

You could also use "first to last" in (4) if that is more accurate.