To me, a proof would have to be a Turing complete procedure for verifying a theorematic result. Often times, proofs, however, only amount to convincing argument

To me, a proof would have to be a Turing complete procedure for verifying a theorematic result. Often times, proofs, however, only amount to convincing arguments (convincing to adepts, that is, who have not yet discovered a flaw in the proof). Furthermore, yes, I truly believe that proofs provided through computational analysis are perfectly legitimate, even if mere humans can hardly cope with them.