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The phrase "the same fact" is correct and can be used in written English.
You can use it to refer to a previously mentioned fact, such as in the following example: At the meeting, we discussed the effects of climate change. The same fact was repeated throughout the meeting - climate change will have serious consequences on our environment if we don't take action soon.
Exact(60)
Occasionally she reintroduces the same fact as if it were new.
Yet, the same fact supported a conclusion in Alexander that plaintiffs were FedEx's employees as a matter of law.
"The same fact reported [by Piketty] holds true for more countries and more years, and more dramatically," the researchers conclude.
439, the same fact has proved not to be dispositive in Alexander and in numerous other California cases where an employment relationship was found.
Other information businesses, of course, are now confronting the same fact, but without the Windows and Office franchises to fall back upon.
That the Hadzabe and the Ju|'hoansi differ as much in their language as in their genetics is a reflection of the same fact.
"Trust issues" or not, our confidence and our exasperation are born of the same fact: the Lakers usually do win, however hard they've made it for themselves.
The same fact checker, Glenn Kessler, also gave the anti-Bain film Four Pinocchios on Friday, calling it a "highly misleading portrayal of Romney's years at Bain Capital".
This assertion may be true, but it may also be false; for the same person may twice learn (from some teacher), or twice discover (i.e. excogitate), the same fact.
Mr. Bernstein emphasizes that "consumer spending as a share of gross domestic product in the United States is about 70 percent," but that's a red herring, because the models of investment and growth also assume the same fact.
(c) lands that would likely have been used as cropland for any 5 out of the last 10 years, immediately preceding such acquisition but for the same fact of ownership or control of the land unrelated to the productivity of the land.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com