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"thus establishing" is correct and usable in written English.
It can be used to indicate that something has been done which confirms or validates something else. For example: "By researching the facts, he was able to further his argument, thus establishing his credibility."
Exact(60)
Thus, establishing the auxin system for multiple proteins can be challenging.
Thus, establishing ntES cell lines provides a better overall chance of cloning animals from endangered species.
Thus, establishing interoperation is a complex task, with many special-case solutions.
They lost $3.5 billion, thus establishing themselves as the federal government's most successful enterprise.
Thus, establishing a microbial system without endogenous fructose transporters would be highly desirable to simplify the assaying of GLUT5 activity.
Thus, establishing an effective and strong safety network between medical facilities is crucial.
Thus establishing a method to measure the condensing capacity of a modular product is necessary.
The channel intends to feature original episodes of shows every Tuesday at 10 p.m., thus establishing a beachhead for new programs.
The first is the one-state solution: offering citizenship to all Palestinians and thus establishing a binational democracy within the entire area controlled by Israel.
We also give an explicit decay estimate for eigenfunctions, thus establishing localization forH in arbitrary spectral gaps ofH0.
In preparation, he and I bought some ridiculously expensive father/son matching swimming trunks, thus establishing a theme of boys-on-tour camaraderie.
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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