As far as I understand the justice system (which, luckily, is not very well), the prosecution is not out to prove your innocence. It goes contrary to all their incentives, both the police and the actual prosecutor. All advice I've ever heard defense lawyers give on this topic points in the same direction: don't count on police or the prosecutor to seek the truth.

I may be wrong, of course. Thankfully, I haven't had the pleasure of finding this out for myself.