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The phrase "and establish this" is correct and usable in written English.
It can be used when you want to indicate the action of setting up or confirming something that has been previously mentioned.
Example: "We need to finalize our plans for the project and establish this by the end of the week."
Alternatives: "and confirm this" or "and set this up".
Exact(35)
Stay tuned as I travel into the field and establish this ambitious research project to inform animal agriculture and land policy!
To achieve and establish this fact, we need to design, demonstrate and incorporate reliable 'passive safety systems' in our advanced reactor designs.
"We*, THE PEOPLE* of the United States, to secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America".
Of course, it never was, and now I would never be able to reach out and establish this small connection to the writer who had given me more joy than anything else in my life.
Taken together with our body size corrected bite force estimates, our results for living and extinct species validate the fearsome predatory reputations of piranhas and establish this group of fishes as a pinnacle of performance in gnathostome jaw evolution.
"We, THE PEOPLE of the United States, to secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America".
Similar(25)
But that's his secret: he has made his career and established this school as a rebuke to all that is snooty about drinking wine.
Dr. Bajestan was the first neuropsychiatry fellow at Stanford University and established this fellowship with Dr. John Barry, her fellowship director and is currently the Associate Neuropsychiatry Fellowship Director.
At Juilliard that seemed particularly poignant, given that Schuman had been the school's president (and later, Lincoln Center's) and established this festival.
More than anyone, Murdoch invented and established this culture in the newsroom, where you do whatever it takes to get the story, take no prisoners, destroy the competition, and the end will justify the means".
July 17 , 1714Berlin, Germany May 26 , 1762Frankfurt an der Oder, Germany Alexander Gottlieb Baumgarten, (born July 17 , 1714 Berlin, Prussia [Germany] died May 26 , 1762 Frankfurt an der Oder) German philosopher and educator who coined the term aesthetics and established this discipline as a distinct field of philosophical inquiry.
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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