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The phrase "able to prove a" is correct and usable in written English.
It can be used when discussing the capability to demonstrate or establish the truth of something, often in a legal, scientific, or academic context.
Example: "The researcher was able to prove a significant correlation between the two variables in her study."
Alternatives: "capable of demonstrating a" or "able to establish a".
Exact(37)
"The police are not able to prove a criminal act.
We then ask a natural question in this paper: What is the minimal (coarsest) abstraction in a given family which is able to prove a set of queries?
With these mathematical test scores in hand, the researchers were able to prove a tangible cost to discrimination of hiring managers.
Getting a bed often depends on a referral from a local agency, which, in turn, depends on being able to prove a local connection.
"So far, nobody has been able to prove a single thing against me," he said after a bail hearing here late last month.
Far more important, it discounted earlier rulings saying that states had to be able to prove "a compelling state interest" for any actions that infringed on religious practice.
Similar(23)
By applying Theorem 2 we are able to prove an existence result also for the general problem (22).
By means of repeated measurement, Mall et al. [50] were able to prove an increase in range of motion of 3.4°.
Moreover, the molecular analyses demonstrating the effectiveness of antagomir treatment were performed at very short times after antagomir injection, whereas we were able to prove an effective downregulation of miR-221/222, and a consequent upregulation of p27, for longer than three weeks.
Yet we are able to prove the A-optimality (in the general class) of these designs using majorisation technique.
While married couples generally share insurance as a matter of right, coverage for a gay partner often hinges on a couple's being able to prove that a domestic partnership exists.
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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