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“indicate the fact” is a valid and usable phrase in written English.
You can use it whenever you need to emphasize that you are referring to something factual. For example, "The results of the experiment indicated the fact that there were no changes in the chemical compound."
Exact(22)
As the statutory language and legislative history clearly indicate, the fact that members of the public view the performance at different times does not alter this legal consequence.
Moreover, his links to social movements indicate the fact that he might be able to point towards a better form of democracy, or a post-parliamentary politics of the future.
This could indicate the fact that there are few jobs in the country to absorb the many graduates the country's universities and polytechnics produce annually.
We refer to evolving digraphs to indicate the fact that the edges are directed, implying the same distinction that exists between graphs and digraphs.
These results indicate the fact that a cell derived from hematopoietic compartment can replicate both ME-7 and RML scrapie strain, but cannot account for neuroinvasion.
Such values indicate the fact that most synonymous mutations occur at the 3rd position, with a few at the 1st position and none at the 2nd as also observed in Australian fish [143].
Similar(38)
The information set is indicating the fact that Player 2 cannot observe whether Player 1 moved up or down.
And on the right, what we see is the frequency content, in particular, indicating the fact that there are several harmonic lines in the tone.
This indicates the fact that the increase in Cr substitution has made the material magnetically soft.
This indicated the fact that agglomerated nanosilica had weakened the cement paste matrix.
This indicates the fact that the active medium is much smaller than the device size, providing a potential of scaling.
More suggestions(20)
refer the fact
indicate the essence
indicate the circumstance
indicate the effect
indicate the question
indicate the factual
advertise the fact
describe the fact
indicate the satisfaction
incorporate the fact
evidence the fact
identify the fact
indicates the fact
identifies the fact
indicate the data
assert the fact
indicating the fact
discern the fact
indicated the fact
ascertain the 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