Proof is showing evidence that something is true; the proof in and of itself does not make something true.
That...is a contradiction.
Originally Posted by Proof - Definition from the Merriam-Webster Online Dictionary
1 a : the cogency of evidence that compels acceptance by the mind of a truth or a fact
b : the process or an instance of establishing the validity of a statement especially by derivation from other statements in accordance with principles of reasoning
We're not doing a Trial by Jury, juries can be wrong, we're talking cold hard facts.