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The phrase "that obtains" is correct and usable in written English.
You can use it to indicate that something exists, has been reached, or is available. For example: "The results of the study demonstrate that a positive correlation exists between happiness and good health that obtains across gender, age, and education."
Exact(60)
"Formation Properties owns real estate and leases it to an unaffiliated third party that obtains a license to operate it as a health care facility," Formation said.
The professor comments upon the extraordinary relation that obtains between the appearance of the moon (its apparent size) and the posture of the observer.
A country that obtains loans from the World Bank, for example, must agree to adjust its economic structure, liberalize its economy, and increase its international financial accountability.
Any fact that obtains is a fact that grounds F. Since F is itself a fact that obtains, F grounds itself.
And D3 is the distribution that obtains when A is entirely emancipated.
Compare for instance the relation of ownership that obtains between a person and her bank account.
The same interdependency that obtains horizontally between the constituents of the cosmos also obtains vertically.
In this picture, the actual world is the possible world that obtains.
These ideas have been implemented in an algorithm that obtains better results than previous approaches.
Ethane is a fluid that obtains a large net power increase when used in mixtures.
We recommend a method that obtains a bootstrap RSS from the observations.
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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