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The phrase "demonstration for" is correct and can be used in written English.
It is often used to describe something that is being done in order to illustrate or prove a point. For example, you could say, "The teacher performed a demonstration for the class in order to show them how to use the new recipe."
Exact(58)
"This is a demonstration for our freedom".
A man did a demonstration for us.
Iraqi commandos even staged a live-fire demonstration for him.
I didn't stay in the demonstration for very long.
At the Mahamasina Square, a demonstration for Mr. Ravalomanana.
In response, to those who have proposed matching demonstration for demonstration for demonstration, and crowd for crowd, I have counseled patience and forbearance.
"He feels he has to be a conqueror, a leader, a demonstration for other men.
She hopes to persuade Bom Jesus to do a demonstration for her class.
It said the interception was not a weapons test or a demonstration for potential adversaries.
They called their own demonstration for Wednesday afternoon outside of the palace.
Talk story about the Vietnam Moratorium demonstration for peace on Oct. 15.
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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