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The phrase "instance is found" is correct and usable in written English.
It can be used when referring to a specific occurrence or example that has been identified or discovered.
Example: "In the analysis, when an instance is found, it is crucial to document the details for further study."
Alternatives: "case is identified" or "example is discovered."
Exact(8)
A protein called HER2, for instance, is found on many breast and other tumors, making it a seemingly good target.
The regulatory interest of the State in this instance is found in the potential for abuse inherent in the union plan.
Many butterfly names are inaccurate – the Essex skipper, for instance, is found far beyond that county – and some are becoming more so.
If such instance is found, it is declared as "FOUT" and all such common instances are stored in "FOUTVECTOR".
An example of this, for instance, is found in Clough and Wood-Robinson (Clough and Wood-Robinson 1985b; they interviewed 84 English (UK) students (aged between 12 and 16 years).
One such instance is found in the first sentence of "The Metamorphosis".
Similar(52)
Corinthians, for instance, was found to have lied about job-placement rates nearly a thousand times.
Few, for instance, are found near the critical regions known as homeobox gene clusters.
At least 19 of PwC's audits, for instance, were found to include deficiencies.
Terms smaller than 0.000000001, for instance, are found from the 1,000,000,000th term onward.
One instance was found on a personal computer in a hospital and the other on a private citizen's home computer.
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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