A question about zkrollup batch submission

For zkroolups, there's someone who submits the batches to the mainnet. What prevents it from submitting conflicting information?

For example, A has 10 eth on the side chain. A signs two transactions A -> B 10 eth, A -> C 10 eth. The side chain operator first submits a batch including A -> B 10 eth to the mainnet. Then the operator submits more batches including A -> C 10 eth without A -> B 10 eth to some other nodes/miners of the mainnet and let the batches propagate?