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The phrase "are pretty established" is correct and usable in written English.
It can be used to indicate that something is well-known or widely accepted, often in a casual or informal context.
Example: "The theories about climate change are pretty established in the scientific community."
Alternatives: "are well established" or "are quite established".
Dictionary
are pretty established
adverb
Somewhat, fairly, quite; sometimes also (by meiosis) very.
Exact(2)
Because they all do proper club gigs, and are pretty established," said Amy Kirwin, associate development officer for museum events and visitor services at the museum.
These guys are pretty established in the cloud space.
Similar(57)
I think the labor pool for this industry is pretty established".
And it's pretty established that it's the gateway to curing and treating a lot of diseases, but especially Parkinson's because it's so specific a problem.
They were pretty established as a gang about 15 years ago if not longer with many branches located here in the city of Chicago.
"I would think all of those things are pretty firmly established aspects of her legacy, regardless of this matter".
The basics are pretty much established, though: people, so long as they're poor enough, will internally ferry sufficient drugs across borders to kill themselves 60 times over.
And the reasons it is unrealised are pretty well established.
He added: "I think what is happening here is we are pretty well established, we are the best party on the planet and people are here from all over the world.
Note to Bobby Jindal Barack Obamaa has in fact been Commander-in-Chief for six years, so his qualifications for the job are pretty well established.
"This is really not true; the basic tenets of a healthy diet are pretty well established and there is a good consensus about those tenets.
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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