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The phrase "a cross section of established" is correct and usable in written English.
It can be used when referring to a representative sample or a diverse selection of something that is already recognized or accepted.
Example: "The study provided a cross section of established practices in the field of education."
Alternatives: "a representative sample of established" or "a diverse range of established".
Exact(1)
With high profile names like Shepard Fairey, Daze, Dan Witz, the Guerrilla Girls and Kara Walker on this years list of artists donating to the auction, the program boasts a cross section of established and emerging Street Artists, graffiti artists, culture jammers and truth tellers who heartily support this program that since 2012 has given more than 400 city youth a second chance.
Similar(58)
a A cross section of the graft.
Figure 1 shows a cross section of a flow control valve and establishes its basic working principle using particle excitation.
The book's characters are a cross section of Hispanics.
But it was not a cross section of Israeli society.
Figure 8 shows a cross section of a heterojunction FET.
But trains allow you time to meet a cross section of your fellow passengers, a cross section which, hopefully, reflects local society.
A cross section of the ocean basin was represented.
"I bought a cross section of 10 independent oil companies".
Nor are they a cross section of their communities.
A cross section of that tree was placed in a Nevada casino".
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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