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The phrase "demonstrate a" is correct and commonly used in written English.
It is typically used to indicate showing or proving something in a concrete or tangible way. Example: The scientist was able to demonstrate a clear connection between the two variables through her experiment.
Exact(60)
Can Mr. Obama demonstrate a comparable magic?
But she did demonstrate a universal truth.
Recent seasons demonstrate a steady decline in net spend.
Read together, these pieces demonstrate a few things.
All applicants must demonstrate a basic competence in English.
These attacks do not demonstrate a reciprocal attitude toward peace.
But they also demonstrate a whole lot more.
As Thermos flasks demonstrate, a vacuum is a great insulator.
Each week, the hosts demonstrate a different technique.
Practical projects such as these can demonstrate a major impact.
The UK continues to demonstrate a strong bookings performance.
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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