As in how does one prove he did not rape a woman? Sure there is: a complete lack of physical evidence and a dearth of circumstantial evidence would prove that no rape occurred. That's what's so perplexing to me about this story: if, as the story claims, there was absolutely no physical evidence whatsoever that a rape took place, why (1) did the cops believe the woman's story, and (2) the prosecutor agree to take on the case?
More accurately, why does he HAVE to? Our criminal justice system is founded on the doctrine of presumptive INNOCENCE; the burden of proof is on the prosecution.
In other words, the defendant doesn't have to prove he DIDN'T commit the crime; the prosecution has to prove he DID.
Law enforcement people get on tears about some things, and as they spend all of their time dealing with crooks, they tend to assume that everyone is a crook. It is best to stay away from them.