In Grokking Bitcoin on page 7, it is noted that:
Invalid transactions are dropped. They will not reach further than the first node.
If so, why do nodes after the first node continue to validate the transaction? If the node is not the first node to receive the transaction, doesn't that mean its valid -- otherwise it would not have reached further than the first node.
Can't the nodes just receive a broadcast of the tx and save themselves from the redundant verification?