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Discover LudwigThe phrase "are thereby" is correct and can be used in written English
It is typically used to indicate that something is being accomplished or affected by the action or state described in the previous part of the sentence. Example: By following this diet plan, you are thereby improving your overall health and well-being.
Dictionary
are thereby
adverb
By it, by that.
Exact(60)
Profits are thereby boosted massively.
Crystalline solids are thereby formed.
Parametric studies are thereby facilitated.
Zombies and other market failures are thereby prevented.
If beliefs and assumptions are thereby subverted, so be it.
Mixtures of primary, secondary, and tertiary amines are thereby produced.
Many homeless applicants are thereby being referred back to the council of their previous residence.
The scores are thereby transmitted to the ITF's data partner, Sportradar.
Those who stand up and speak out are thereby treated as criminals.
A number of new insights are, thereby, obtained.
Jump conditions are thereby eliminated, allowing finite-difference discretization.
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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