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I would like to express "under all the assumptions, except a certain one (call this certain one A), of the theorem, we construct...". If it can be shortened, then the first thought that came to me was "under all but the A assumptions of the theorem, we construct...". However, this seems not grammatical and confusing.
Is my evaluation true? If not, what would be a better option out there? Thanks.
One of the problems in your original sentence is that your use of commas creates parenthetical information. You don't want to do that because you've put except inside that parenthetical information. That makes it nonessential when it actually is essential to what you want to say.
Your revised sentence is talks about A assumptions (plural), yet you've previously indicated that there is only a single exception. (Perhaps the s is a typo.)
I suggest this:
Under all but one assumption of the theorem (call the exception A), we construct . . .
What's in parentheses can be removed without causing harm to the sentence. It's up to you if you want to mention that you're going to call the exception A or not.
