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The phrase "as duly" is correct and usable in written English.
It is typically used to indicate that something is done in a proper or appropriate manner, often in formal contexts.
Example: "The documents were submitted as duly required by the regulations."
Alternatives: "as required" or "as appropriate".
Exact(7)
Much of the time these chief executives function in a democratic tradition as duly elected public officials.
The Democratic party elite tried to force him to stand down as duly elected nominee, but backed off when they realised they had no power to do so.
Since the 90s, the most prominent new arrivals have been from eastern Europe and they, like their predecessors, come with a small criminal class attached, as duly enacted in David Cronenberg's 2007 film, Eastern Promises.
Smotrich River Yet 73 years ago this week, in the space of three days, 23,600 Jews were slaughtered in the forests, fields and copses surrounding Kamyanets-Podilsky, as duly reported in bureaucratic mission-accomplished fashion by local SS leader Friedrich Jeckeln to his boss back in Berlin, Gestapo chief Heinrich Himmler.
The observation is not entirely novel because integrated pararetrovirus sequences have been reported previously in other plant genomes (petunia and rice) as duly cited in this manuscript.
This finding exemplifies the need, as duly noted by Komar et al., that experimentally derived competence indices should be consolidated with field data to better estimate host potential (5 ).
Similar(52)
After being digested in various acronymic gullets, this campaign produced not only new zoning text (sections ZR81-832 and ZR81-85, as Sagalyn duly notes) but, as an enforcement mechanism, an entirely new unit of measurement: the luts, or "Light Unit Times Square".
There is talk of moving up elections so when an Iraqi official is assassinated, he is not seen as a person working with the U.S., but as a duly elected representative of the Iraqi people.
Berry's autobiography, as Cohodas duly notes, denies it.
He was 64 – one year, as was duly observed, for each square of the chess board.
Despite his grand manner, Irving, as Guttenplan duly finds out, is not upper class at all.
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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