The phrase "ability to prove a" is correct and usable in written English.
It can be used when discussing someone's capacity or skill to demonstrate or establish something, often in a formal or academic context.
Example: "The scientist's ability to prove a hypothesis is crucial for the advancement of research in the field."
Alternatives: "capacity to demonstrate a" or "skill to establish a".
The success of the deal rests on both Greece's ability to process thousands of people in a short space of time, and Turkey's ability to prove itself a safe country for refugees.
But there must remain a major doubt over the 28-year-old's ability to prove his fitness for a Test in a single, low-key fixture between the EPP and the Queensland second team at the Allan Border Oval.
"These factors," he continued, "played a significant part in the people's ability to prove their case beyond a reasonable doubt and had the effect of eviscerating the credibility of those prosecution witnesses.
Jurevicius' future in the N.F.L. is tied to his ability to prove he can be a reliable possession receiver who knows how to use his 6-foot-5, 230-pound frame in tight quarters.
Various study designs have a differential ability to prove cause and effect relationships, and will similarly have a differential ability in validating the usefulness of genetic markers.
Even without the ability to prove your income, you might help a lender be more willing to make you a car loan if you provide other financial statements that reflect your overall worth.
Next month's Commonwealth Games in India are a big test of Delhi's ability to prove itself on the world stage - a test that some would argue it is already failing.
What they also have in common, of course, is a supreme ability to prove from time to time they are well worth the trouble.
The government's case hinges upon its ability to prove that the defendants knew of an impending implosion of the subprime market, yet deceived investors with a different much more positive story.
