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The phrase "of fact" is correct and commonly used in written English.
It is typically used to refer to a statement or information that is proven to be true or based on evidence. Here is an example: "The lawyer presented a list of facts to support his argument in the court case." In this sentence, "of fact" is used to clarify that the lawyer presented evidence or information that is factual and not based on opinions or assumptions. It can also be used in other contexts, such as "in fact," "matter of fact," or "fact of the matter."
Exact(41)
Your next ball of fact.
Cashman was matter of fact.
It's so matter of fact.
It is, rather, a statement of fact.
(Kristof) This is an error of fact.
The painting is chillingly matter of fact.
Similar(17)
It is matter-of-fact.
It was matter-of-fact.
Her tone was matter-of-fact.
His voice was matter-of-fact.
Tebow was more matter-of-fact.
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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