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The phrase "as have been" is correct and usable in written English.
It is usually used to refer to something that has already been mentioned, or to emphasize that something is part of a repeated pattern. For example: "The results of the poll are consistent with previous surveys, as have been the reactions to the news."
Exact(60)
But they may just as well as have been sheep.
There are significant benefits to the free market, as have been proven due to existing institutions.
Chilcot must not make the same mistakes as have been made before.
But their tools are the same as have been used for hundreds of years.
Eight of the first fourteen Presidents were Episcopalians, as have been half of the Chief Justices.
Over the lifetime of the plant's operation over 3000 tonne of As have been emitted into the environment.
The Iranian motives behind such arrests have been unclear, as have been the political machinations over them.
Between them, Clemens and Maddux have seemingly won nearly as many Cy Young awards as have been awarded.
And they wonder whether their future is going to be prosperous and bright, as have been our lives.
All three are African-Americans, as have been all mayors elected in this majority-black city since 1973.
But there is enough known to make the assertion of such universal features as have been given with fair confidence.
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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