[oldnews193]

> Verification is at least as complicated as writing the program you are verifying.

I guess, writing a proof is basically like writing a program. Then checking a proof ought to be like *running* a program, not proving an arbitrary property of it. If your proof/program evaluates to "false", it's a wrong proof. So this is all a question of having an appropriate semantic model of computation/proof-checking, on which you can check your proof.

You could then ask: "why is it that I can always run a proof? What if running it does not terminate?" To which I'd have to admit that I am really, seriously not an expert on this, but I vaguely recall that interactive theorem proving systems like Coq have a non-Turing-complete type systems. Maybe it's for a relevant reason?