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The phrase "consistent with the fact that" is correct and usable in written English.
This phrase is typically used in an argumentative or informative context, where one is trying to prove a point. For example, "The evidence is consistent with the fact that the defendant was guilty of the crime."
Exact(60)
This is consistent with the fact that human sleep consists of repeating sleep units.
This is hardly consistent with the fact that these officials have offered another building.
And that, again, is a smoother reconstruction consistent with the fact that the triangles are smoother than the rectangles.
A second is subtracted off to keep consistent with the fact that the state machine is a second behind reality.
This is consistent with the fact that memory shows pronounced deficits in SZ, with working memory primarily affected22,47.
We uncover little effect of subsidies on academic researchers, consistent with the fact that their incentives are unaffected.
This is consistent with the fact that the nozzle ablation was mainly diffusion-limited when the wall temperature was high.
This is consistent with the fact that these effects are primarily the result of the interaction between inclusions.
This is consistent with the fact that our sample over-represents large employment websites.
This is consistent with the fact that long-chain alkanes are prone towards cracking.
which is consistent with the fact that the maximum of γ ( t ) blows up with β.
More suggestions(15)
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consistent with the negativity that
consistent with the law that
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consistent with the finding that
consistent with the proposal that
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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