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The phrase "as well established" is correct and usable in written English.
It can be used to indicate that something is recognized or accepted as true or valid, often in a formal or academic context.
Example: "The theory is as well established in the scientific community as the laws of physics."
Alternatives: "firmly established" or "widely recognized".
Exact(42)
It is true that the phrase is not as well established as, say, the Monroe Doctrine.
The principles of global warming are as well established as any in physics.
"Evolution is a fact, a fact as well established as apples falling down.
Company had, in effect, treated as being as well established as the principle of absolute power.
But to this rule there is an exception, as well established as the rule itself, viz.
A trend as well established as this can be halted only by a new social attitude.
Similar(18)
They are not as well-established in social and behavioral research as they are in biomedical research.
That counts as well-established compared to its near neighbour the Bluebell vineyard which only began production in 2007 and started winning awards by 2011.
But because they were going for people who weren't as well-established – and probably cheaper as well, let's be honest – it's harder.
When you're as well-established as Michael's, it's hard to both keep an edge and satisfy the regulars, but that appears to be the case here.
But her race has attracted national attention as an example of progressive candidates bristling as well-established Democratic organizations backed their rivals.
More suggestions(18)
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com