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The phrase "correctly showed" is correct and usable in written English.
It can be used when indicating that something was demonstrated or presented in an accurate manner.
Example: "The experiment correctly showed the relationship between temperature and pressure."
Alternatives: "accurately demonstrated" or "properly illustrated."
Exact(17)
In copies printed later, the map correctly showed the missionaries' town, Iquitos.
As an accompanying map correctly showed, Dieppe is east of the D-Day beaches, not west.
As an accompanying map correctly showed, they are 60 miles south — not north — of the Sawtooths.
As an accompanying map correctly showed, it is northwest of Santiago, not southwest.
By contrast, on the Democratic side, most pre-primary polls correctly showed Mr. Gore leading Bill Bradley but in several cases by double-digit margins.
As an accompanying map correctly showed, it will be on the southwest corner of the park, not the southeast.
Similar(43)
The film correctly shows that Jameson went ahead on his own initiative.
It is No. 8. ("Payback," by Fern Michaels, is correctly shown as No. 5).
As the film correctly shows, reporting from Vietnam had been tightly controlled.
The United States statistics, more correctly, show them under a separate heading.
The film correctly shows that the accent was so thick, and his speech so hesitant, that Turner could not always be understood when giving lectures.
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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