"There are no" vs "there are not any"
We're disputing the use of "there are no lobsters" versus "there are not any lobsters", with the assertion that, in the first example, as soon as you say "there are" you have established the presence of lobsters, so you cannot then go on to say that no lobsters are there.
Are these two statements totally equivalent, or is the first one invalid unless there are actually some lobsters?