"A/the proof" is most commonly used to refer to an actual formal mathematical construction, i.e. a proof of a mathematical theorem.
As Erik noted, your friend's sentence is correct, but it is the more informal use of the word 'proof,' meaning 'evidence.' When used in this sense, the article is usually excluded.
Really, the word 'evidence' would have been a better choice here, but 'evidence' and 'proof' have unfortunately become conflated in modern usage. I say it is unfortunate because the formal usage actually refers to a related but quite different concept. With a proof (in the formal sense of the word,) if the proof is constructed correctly, it is not possible for the conclusion to be false if the premises on which it is based are true.
Proofs require either deductive reasoning or exhaustive induction to be used. Evidence, on the other hand, can be interpreted to suggest a conclusion, but doesn't actually prove that conclusion to be necessarily true. Such a conclusion is reached via inductive reasoning. This seems to be the case with your friend's assertion.