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The phrase "thereby established" is correct and commonly used in written English.
It is typically used to show that something has been established or accomplished as a result of a previous action or decision. Example: "By implementing these changes, the company has thereby established itself as a leader in the industry." In this sentence, "thereby established" indicates that the company's actions have resulted in its establishment as a leader. Other possible uses of this phrase could include: - "The new law will thereby establish a stricter penalty for tax evasion." - "The successful completion of the project has thereby established our team's credibility." - "The signing of the treaty will thereby establish a framework for international cooperation."
Exact(32)
The rates thereby established are not beyond recall.
And the rule thereby established must be applied to judgments lawfully rendered without a verdict.
They thereby established a decisive edge over the Neanderthals in Europe and, among other advances, the start of representational art.
A high capacity to communicate is thereby established, enabling monitoring without impairing empowerment.
They were about outwardly ordinary lives, and thereby established that there's no such thing as an "ordinary" life; there is only inadequate appreciation of humanity.
Dalton brought these observations together and thereby established a language that, with minor emendation, has become universal in chemistry.
Similar(28)
Later that year he was made administrator of Mashonaland, thereby establishing the first settled government.
This relationship thereby establishes an inverse relationship between wavelength and photonic energy.
These reactions, in turn, sparked central efforts to manage disputes and thereby establish law and order.
Police may install large concrete and metal barriers, thereby establishing zones where protesters cannot congregate and organize.
Tiffany adopted the standards of English silver in 1851, thereby establishing the term "sterling" in the United States.
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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