The phrase "a case that proves" is correct and usable in written English.
It can be used when discussing an example or situation that demonstrates a particular point or argument.
Example: "The study presented a case that proves the effectiveness of the new treatment in reducing symptoms."
Alternatives: "an example that demonstrates" or "a situation that illustrates".
In a case that proves flattery always gets results, Belgian police this week arrested a notorious Somali pirate after convincing him they wanted to make a documentary film about his exploits.
Every once in a while, somewhere in the world, we come across a case that proves either overtly or implicitly that men can get away with things that women can't.
A Los Angeles criminal defense attorney takes a case that proves more complicated and dangerous than he expected.
Even with a case that proves too tricky to be credible -- here, the violent history of a former military man on trial for rape is tied in with the murder in Harlem of an old woman who was at one time the mistress of King Farouk -- Alex saves face with the solid expertise she displays in the courtroom.
Mariano Rajoy, once viewed as the great survivor of Spanish politics, has been ousted as prime minister in a vote of no confidence after several former members of his party were convicted of corruption in a case that proved a scandal too far.
Simply stated, using piecemeal evidence that a dishonest F.B.I. director wanted to keep out of court, Bill Baxley and Doug Jones put together a convincing case that proved beyond reasonable doubt that Alabama juries convicted the right men for murder.
In Romney's case, that proved disastrously true.
Dave, this is another case that proves history is a very controversial subject, and I am not a historian.
It was a complicated case that proved to be drawn out, with a real prospect for Hung's family winning better compensation — though I am unaware of any resolution being made public.
The case has become a cause célèbre for death penalty activists who for years have been searching for cases that prove an innocent person has been executed.
Wheatley has been a police officer for 26 years, and has never encountered a case that has proved so challenging.
