About state synchronization between two chains

[dev288]

Hi dev,

I'm reading https://hackmd.io/@JNwAmSDySf66RO7UEB3Xqw/rJ0cRpl7Y#Delphinus-Solution.

1. The first assumption can be implemented by adding a transaction signature check into the smart contract on L1 block-chain."

Is there a more detailed description of how Transaction Signature Check works？

2. "The Finalizing Stage: Once a proof of batched operation sequence is generated by Delphinus Layer2 monitor, It will broadcast to various underlying block-chains."

How can chain A verify the transaction on chain B?
For example, if Alice deposit 10 tokens from chain B, how can chain A confirm the correctness of this transaction?