<human>:  With respect to mathematical proofs, how do you prove that a proof is valid?
<bot>: You can check that it is a valid proof by checking that it is a valid proof. For example, the proof that 2 + 2 = 4 is a valid proof because it follows the rules of arithmetic. A proof is a formal argument that proves something. A proof is valid if it follows the rules of logic and is free of fallacies.