"With loss of generality" or "not without loss of generality"?

Question

I am writing a research paper in which I have a model. A central point I am making is that parting with a particular assumption (which is prevalent in the literature) yields qualitatively different results. I guess that authors have been using this assumption under the tacit presumption that going away from it would lead to similar results. I show that this is not the case.

Which of the following two expressions is more appropriate to use and drives home the message?

1. ... therefore, the assumption is with loss of generality
2. ... therefore, the assumption is not without loss of generality

I err towards the second one as it is stresses the contrast with the current literature but I am not sure I like the double negation. I am also happy to hear other suggestions.

Answer 1

As I recommended in my comment, I think that a nice alternative would be "the assumption cannot be made without a loss of generality".

Answer 2

I'd go for "not without loss of generality", as "without loss of generality" is a standard phrase (in mathematics, at least), and you are pointing out it isn't true here. But make sure your (superficial) gentle reader doesn't miss the all-important "not".