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The phrase "demonstrates that to" is grammatically correct and usable in written English.
You can use it to introduce a demonstration of something, as in the sentence: "The results of the study demonstrate that to be successful, companies need to prioritize customer service."
Exact(14)
Tom Greatrex, Labour's shadow energy minister, said: "Cameron and Osborne have repeatedly ignored genuine and legitimate environmental concerns – they seem prepared to accept shale gas at any cost, and this letter demonstrates that to be the case.
"It demonstrates that to every Republican who said that marriage didn't matter to the voters, it sure does," said the Rev. Jason J. McGuire, the executive director of New Yorkers for Constitutional Freedoms, a conservative group.
The study clearly demonstrates that to better assess interdomain routing in a continent, it is necessary to perform measurements from a diversified range of vantage points.
This demonstrates that to improve reliability of production and profitability in the prime lamb industry, the pricing strategy, risks and management practices associated with each environment need to be considered.
Our study demonstrates that, to fully understand the microstructure and the property of a nitrocarburized surface, it is necessary to adopt the phase transformation sequence α-Fe + N/C → γ-N/C + N/C → γ′ + N/C → ε, in which the existence of a transitional austenite phase containing N/C atoms (γ-N/C) must be assumed and the γ′ phase actually forms prior to the ε phase.
We note that the non-zero density of TO at the bilayer center in the UNI2 system demonstrates that TO can partition into the bilayer center without an aggregate being present.
Similar(46)
Pro-Najib groups also have plans to demonstrate that day, leading to concerns about potential clashes.
It must demonstrate that to a skeptical world.
We look forward to the opportunity to demonstrate that to the New York Attorney General".
I had friends who were demonstrating that day next to the embassy.
That was its theme and everything in it was dedicated to demonstrating that".
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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