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The phrase "already reported that" is correct and usable in written English.
It can be used when referring to information or findings that have been communicated previously.
Example: "The committee has already reported that the project is on schedule and within budget."
Alternatives: "previously stated that" or "earlier communicated that".
Exact(60)
We already reported that sepsis promoted malignant tumor growth when tumor cells were inoculated in post-septic mice.
Warburg et al (1927) already reported that often glucose metabolism is enhanced in tumours.
We already reported that MAdCAM-1 on colonic endothelial cells after TNF-α stimulation in vitro [ 45].
In these cases, there are potential mechanisms already reported that can be invoked to explain the observation.
Researchers have already reported that gram positive bacteria are much more susceptible to antimicrobial agents as compared to gram negative bacteria [ 12].
Some studies have already reported that inadequate sanitary conditions are associated with anaemia [ 39, 40] as well as undernutrition in children [ 28, 29].
It has been already reported that fluorine (F) could increase DLC antibacterial activity.
We have already reported that chitosan inhibited the growth of cariogenic bacteria in vitro.
Ecological associations have already reported that several hundred rare birds' eggs have been destroyed.
The Chinese press has already reported that sharks have been spotted in the rescue area.
And some politically critical states have already reported that unemployment has broken 10percentt.
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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