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"the former case" is correct and usable in written English.
You can use it to refer to a case that has already been mentioned. For example: "In the former case, the defendant was found innocent; however, this time the jury reached a verdict of guilty."
Exact(60)
In the former case they found none.
We start considering the former case.
Furthermore, in the former case the designs are triplewhist tournaments.
The present work is concerned with the former case.
Males in the former case performed virtually identically to those tested in experiment 1.
Each compensation loop is similar to that in the former case.
In the former case, however, it does pose significant interpretation challenges.
In the former case the detection of corrosion has to be performed in reinforced concrete.
In the former case, the spatial resolution was about 20 μm.
In the former case, the background of lean manufacturing and its major implications are reviewed.
The area of magnetic classification within magnetic separation bears on the former case.
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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