"It holds+statement"
In some of the mathematical papers I've encountered sentences like "It holds A>B.". I have a feeling that this is far from being grammatically correct, but I would appreciate a confirmation (or negation) by native English speakers, in order to have a reference.
This is similar, but in my opinion a bit more striking than "It holds that A>B.", cf.
ELU: Is "it holds that" correct?
Mathematics: Is there a better alternative to the phrase 'it holds that'?
Solution 1:
It's grammatically correct if you omit the that and this is often done in math; however, I suggest you keep it.
...which implies that in these regions holds [equation].
... we observe that it holds [equation]
Now, since it holds [equation] ref (an IEEE publication)
...for every pair...it holds [equation] ref
Then it holds [equation] ref
Obviously, it holds [equation] ref
We don't always see that after it holds and it follows:
Note that in our structure, Bob knows whether p3 holds each state (i.e. if it holds he knows it and if it doesn't hold he knows the negation of it). N. Gal-Oz and P. R. Lewis; Trust Management XII
It holds he must be free to earn, spend, to save, to accumulate property that may give protection in old age and to loved ones. Herbert Hoover in Gateway to Citizenship
The only things in Hume's system that he holds we cannot misrepresent are those that are 'immediately present' to the mind. Donald Rutherford; Oxford Studies in Early Modern Philosophy, vol. X
But he holds we cannot now silence the apprehension that there may be one. G. H. Howison; The Limits of Evolution
It is true that if he holds we must deal with poetry after this fashion, it is because he sees ambitious possibilities in poetry, and conceives getting the most out of a poem in a way all his own. John Constable; I. A. Richards and His Critics V10
Ethical naturalism is non-reductive in the strong sense that it holds we cannot move from the 'is' of empirical science to the 'ought' of moral theory. Tom Angier; The Cambridge Companion to Natural Law Ethics