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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def verify(self, proof, challenge, state):
 """returns true if the proof matches the challenge. verifies that the server possesses the encoded file. :param proof: the proof that was returned from the server :param challenge: the challenge provided to the server :param state: the state of the file, which includes the merkle root of of the merkle tree, for verification. """

        state.checksig(self.key)
        if (proof.leaf.index != challenge.index):
            return False
        return MerkleTree.verify_branch(proof.leaf,
                                        proof.branch,
                                        state.root)