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The phrase "are presented to demonstrate" is correct and usable in written English.
It can be used when introducing examples or evidence that illustrate a particular point or concept.
Example: "The results of the study are presented to demonstrate the effectiveness of the new treatment."
Alternatives: "are shown to illustrate" or "are provided to highlight".
Exact(60)
Two examples are presented to demonstrate the main results.
Finally, numerical examples are presented to demonstrate the theoretical analysis.
Some illustrative examples are presented to demonstrate this theory.
A number of examples are presented to demonstrate this concept.
Numerical results are presented to demonstrate the proposed approach.
Illustrative examples are presented to demonstrate this proposed approach.
Two case studies are presented to demonstrate this approach.
Simulation results are presented to demonstrate the control design procedure.
Experimental results are presented to demonstrate the method.
Two numerical examples are presented to demonstrate the proposed method.
Data and examples are presented to demonstrate the functionalities.
More suggestions(12)
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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