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Discover Ludwig"finally by" is a correct and usable phrase in written English
You can use it to indicate that something was completed or accomplished by someone or something after a long time or after overcoming obstacles. It can also be used to express a sense of relief or satisfaction. Example: "After months of hard work and dedication, the project was finally completed by the team."
Exact(60)
Finally, by aggregating all individual pairs of predicted interactions, the final network was obtained.
Finally, by noon Friday, Borghei was ready to give up.
A silence developed which was broken finally by the Western Union young lady.
Finally, by dint of running errands for them, he gains entry into their house.
Finally, by chance, Ben discovers the notebooks that Jakob has left.
It was remarkable that he lost the title, finally, by only three points.
Finally, by a further strange osmosis, two teams emerge for a "national championship game".
He was succeeded by Scott Bryan, and then by Dan Silverman, and finally by Mr. Gurvich.
The two stages of the process of speciation can be characterized, finally, by outlining their distinctions.
Finally, by the introduction of a statute in 1864, complete freedom of enterprise became a reality.
The future has arrived, finally — by the prosaic hand of our cellphones.
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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