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"is finally established" is a correct phrase and can be used in written English.
It is usually used to describe when something has been firmly or officially confirmed or settled after a period of uncertainty or change. Example: "After years of research, the cause of the disease is finally established." "The new company policy is finally established after much debate and consideration by the board." "In the court case, the truth about the crime is finally established through key evidence." "In the final chapter of the book, the fate of the main character is finally established."
Exact(12)
A systematic design methodology is finally established, in consideration of the inherent loudspeaker dynamics.
I hope that when this rule is finally established, goalies will be allowed to handle the puck below the goal line, but will be prohibited from moving it above the goal line.
Moreover, aiming at the unmodeled dynamics and completely unknown nonlinear functions which have Markovian jumping features, several two-layer neural networks (NNs) are introduced for each mode and the adaptive backstepping control law is finally established.
This operation is repeated for all other links until the entire IMAP is finally established.
The model of online load-stress relationship that is highly suitable for line stress calculation is finally established.
In this case, both the voltage and current supplied is highly unpredictable until reliable physical contact is finally established.
Similar(48)
The West Bank economy is booming and the Palestinian Authority is finally establishing the rule of law.
Exactly that was finally established in 2009.
The park was finally established in 2010.
Specific boundary conditions are finally established.
It was finally established that Dr. Tobien's mastodon was Peale's.
More suggestions(14)
is finally implemented
is definitively established
is finally tested
is conclusively established
is finally acknowledged
is eventually established
is finally incorporated
is ultimately established
is recently established
is finally achieved
is finally provided
is finally determined
is now established
is has established
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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