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"As has been shown" is correct and usable in written English
You can use it when you are summarizing or referring to facts or evidence that have already been presented in the same context. For example, "Studies indicate that exercise leads to improved health outcomes. As has been shown, exercise leads to a decrease in stress levels and an increase in emotional wellbeing."
Exact(60)
Russia's mentality is too easy to shape, as has been shown over and over".
"The potential for growth in Spain is huge, as has been shown in the past few years.
Diverse teams make better decisions, as has been shown time and again by research.
We suggest that the nonconsumptive effects of parasites might overshadow their consumptive effects, as has been shown for predators.
Type 2 resin pockets are formed in response to damage to the cambium, as has been shown by Donaldson (1983).
Clearly not all people in Sderot agree with these views, as has been shown.
This will dramatically increase the health and safety of sex workers, as has been shown in New Zealand.
The researchers write that thyroid hormones may influence the apes' behavioral responses to stress, as has been shown in other animals, like humans, dogs and rodents.
We tested whether color could automatically bias selection, as has been shown previously with contrast [15].
We sought to discover if this was the case in Drosophila, as has been shown for other proteins[48], [49].
We were unable to generate secondary spheres from the initial spheres, as has been shown for other tissues.
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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