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The phrase "a demonstrable case" is correct and usable in written English.
You can use it when referring to a situation or example that can be clearly shown or proven to exist or be true.
Example: "The researcher presented a demonstrable case of the effects of climate change on local ecosystems."
Alternatives: "a clear example" or "a provable instance".
Exact(3)
Here was a demonstrable case of promises made (if you have faith, you can move a mountain) but not kept (the mountain not only stays put but suddenly erupts and consumes a few villages).
Dems should NOT commit to impeachment unless & until there's a demonstrable case for one.
David Axelrod, a former senior adviser to Barack Obama, urged Democrats "NOT commit to impeachment unless & until there's a demonstrable case for one".
Similar(56)
There is a demonstrable cause in the majority of cases, usually an intraluminal neoplasm.
Sarcoma most typically presents spontaneously without a demonstrable cause.
We continue to see demonstrable cases of systemic gender discrimination -- even in this day and age, when women have come so far.
"The reckless conduct in this case poses a demonstrable risk to the safety of the public if Dr Murray remains out of custody on bond".
Secondary AIHA, that is, cases with a demonstrable associated or underlying disease, accounts for about 50% of w-AIHA, while the remaining 50% are classified as primary.
Diagnosis was confirmed through review of all potential H&E stained slides and cases with a demonstrable pre-existing PSA or its 'ghost' were included in the study (n=24).
The clinical profile of HCDD is very similar to that of other MIDD, except for a higher incidence of hypertension and less-frequent association with either a demonstrable plasma cell dyscrasia (∼25% cases when compared with 50% cases of LCDD) or circulating monoclonal free light or heavy chain [ 7].
A total of 28 cases (75.7%) had a demonstrable lead point.
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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