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The phrase "are demonstrating for" is correct and usable in written English.
It can be used when referring to people who are actively showing support or advocating for a cause or issue.
Example: "The students are demonstrating for climate action outside the university."
Alternatives: "are advocating for" or "are protesting for".
Exact(6)
"They have shown the way they want to live and are demonstrating for a better future.
Similarly, Alexey Gordienko's photograph "Demonstration, Leningrad" (1988) feels pertinent — although the exhibition does not include a translation of the placards carried by the activists or any description of what they are demonstrating for (or against).
"We are demonstrating for nine months, and will keep demonstrating for another month, to let our Arab brothers and the world see how peaceful our uprising is," he said.
"The emergence of beauty how-to videos on YouTube is a very good indicator of the overall volume of interest that women are demonstrating for beauty video content online," said Marisa Thalberg, the vice president of global online marketing for the Estée Lauder Companies.
The brave souls of Liberation Square are demonstrating for a worldwide audience that, in spite of Obama, hope soldiers on.
What I find is that before going on stage, we can tell ourselves all these stories about what could happen, which causes anxiety and fear, when in actuality we are demonstrating for three minutes in front of very supportive people.
Similar(54)
Results are demonstrated for compliant gear applications.
Simulations results are demonstrated for illustration.
Several benchmark examples are demonstrated for verification purposes.
Such improvements are demonstrated for several test cases.
Promising results are demonstrated for a typical power plant.
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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