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The phrase "able to establish that" is correct and usable in written English.
You can use it when discussing the capability to demonstrate or prove a particular point or fact.
Example: "The researchers were able to establish that the new treatment significantly improved patient outcomes."
Alternatives: "capable of demonstrating that" or "able to prove that".
Exact(59)
"If I've been in some way able to establish that, that's great".
It was important we were able to establish that enthusiasm to sense from the player and his people.
An Observer investigation has also been able to establish that parliament has not been told the full extent of the problem.
And it is all the stranger when you consider that no serious scientific study has been able to establish that electrosensitivity exists.
A photographer at the Georgia Gazette, Richard Somers, suspected that Mercer had been kidnapped, and he and the paper's publisher, Albert Scardino, were able to establish that fact.
We were also able to establish that commonly reported artifacts of electric field stimulation are not the primary mediators of the observed effects.
We were also able to establish that Frank Koza does work for the NSA and could confirm his senior post in the Regional Targets section of the organisation.
At that time the chemical nature of enzymes was unknown, but through his research Northrop was able to establish that enzymes obey the laws of chemical reactions.
The Afghan administration will not be able to establish that authority unless financial and military aid to warlords ceases in favor of an effort to build national security forces.
Drawing on the help of the Guardian Money desk - plus a few calls to the Revenue press office - we were able to establish that Carolyn will, after all, probably qualify for tax credits (see right).
Similar(1)
The researchers were able to establish that--as with humans--differences in shared environments (in this case, different zoos) did not influence the happiness differences.
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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