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Discover Ludwig"have subsequently" is correct and usable in written English.
You can use it when talking about what happened after something else; either immediately or at a later point in time. Example: After we identified the problem, we have subsequently researched potential solutions.
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Poverty levels were extremely high and have subsequently declined significantly.
A number have subsequently taken up direct employment with Quebecor".
It also claimed to have subsequently found a "discrepancy".
They have subsequently rebounded, closing at 1,216 pence Tuesday.
Any number of Afghans we've armed have subsequently deserted.
Everything we have subsequently discovered invites more urgency not less.
Other local NHS employers have subsequently joined the initiative.
Some have subsequently seen him, erroneously, as a traditionalist.
What about if all personnel have subsequently moved on?
I have subsequently had this diagnosed as plantar fasciitis.
In every other country, gun massacres have subsequently become rare.
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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