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The phrase "an example supporting" is correct and usable in written English.
It can be used when introducing a specific instance or illustration that backs up a claim or argument.
Example: "In the discussion about climate change, an example supporting the need for immediate action is the increase in extreme weather events."
Alternatives: "a case illustrating" or "a demonstration backing".
Exact(7)
It cited the 1971 Gay Liberation Front manifesto as an example supporting this position.
In this section, we give an example supporting Theorem 3.1.
This published study should be seen as an example supporting the arguments demanding revision of the regulatory framework mandating self-control of biotech industry products.
He quotes at length passages of "dramatic beauty", and also finds occasion to use this play as an example supporting his characterisation of the general nature of Shakespeare's genius, and the relation between morality and poetry.
There is a report of fixation of an inactive form of caspase 12 by a nonsense mutation (rs497116) in non-African populations[43], and this is an example supporting the 'less is more hypothesis'[44].
As it appears that neural responses might be also described by a hierarchical representation [38], [40], we choose an example supporting this view, with neural subpopulations responding to either single perceptions or multiple selective combinations of face perceptions (See illustration in Figure 1C).
Similar(53)
Finally, a numerical example supporting our theoretical predications was given.
Finally, a numerical example supporting the theoretical analysis is given.
A numerical example supporting our main result is also given.
The final section of the paper contains a numerical example supporting the result.
A good example supporting the value of data integration is the current lack of driver and pressure data for REDD planning.
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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