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The phrase "a well-established" is correct and usable in written English.
It can be used to describe something that is recognized, accepted, or firmly rooted in a particular context or field.
Example: "The company is a well-established leader in the technology industry, known for its innovative products."
Alternatives: "a firmly established" or "a widely recognized".
Exact(56)
Then a well-established pattern repeated itself.
"That's been a well-established rule".
National reconciliation is a well-established concept.
A well-established healthcare system has disappeared.
Novelty is a well-established sexual stimulant.
And it is a well-established one".
Rentería is a well-established hitter.
Similar(4)
A trained architect, Hardwicke is a well established production designer.
We are a well established small animal practice in Helena.
It is a well established, but not incident-free, science.
Alcohol is a well established breast cancer risk factor [19].
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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