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I mean tx4, tx5, tx6 are txs sent from Shard 0 to Shard 1, and they need to be executed in shard0 and shard1, right? So what's the difference of the execution between shard0 and shard1?
Execution of a cross-shard transaction (minus in the balance of sender) is done first in sender's shard, as sender's shard has all means to validate the transaction, afterwards if validated it is included in sender's shard block and then the header of the block holding this transaction is sent to be notarized by the metachain.